Graphical Analysis

Author

Josie Athens

Published

February 14, 2024

2 Data

The Western Collaborative Group Study (WCGS) is a well known prospective cohort study. Male participants aged 39 to 59 from 10 California companies were originally selected to study the relationship between behaviour pattern and the risk of coronary heart disease (CHD).

wcgs = read_rds("data/wcgs.rds") |> rcopy
wcgs |> schema
┌──────────┬───────────────────────────────┬────────────────────────────────────
│ names    │ scitypes                      │ types                             ⋯
├──────────┼───────────────────────────────┼────────────────────────────────────
│ id       │ Count                         │ Int64                             ⋯
│ age      │ Count                         │ Int64                             ⋯
│ height   │ Continuous                    │ Float64                           ⋯
│ weight   │ Continuous                    │ Float64                           ⋯
│ sbp      │ Count                         │ Int64                             ⋯
│ dbp      │ Count                         │ Int64                             ⋯
│ chol     │ Union{Missing, Count}         │ Union{Missing, Int64}             ⋯
│ beh_pat  │ Multiclass{4}                 │ CategoricalValue{String, UInt32}  ⋯
│ ncigs    │ Count                         │ Int64                             ⋯
│ dib_pat  │ Multiclass{2}                 │ CategoricalValue{String, UInt32}  ⋯
│ chd      │ Multiclass{2}                 │ CategoricalValue{String, UInt32}  ⋯
│ type_chd │ Multiclass{4}                 │ CategoricalValue{String, UInt32}  ⋯
│ time     │ Count                         │ Int64                             ⋯
│ arcus    │ Union{Missing, Multiclass{2}} │ Union{Missing, CategoricalValue{S ⋯
│ smoker   │ Multiclass{2}                 │ CategoricalValue{String, UInt32}  ⋯
└──────────┴───────────────────────────────┴────────────────────────────────────
                                                                1 column omitted

The kfm data frame was collected by Kim Fleischer Michaelsen and contains data for 50 infants of age approximately 2 months. They were weighed immediately before and after each breast feeding. and the measured intake of breast milk was registered along with various other data.

kfm = read_rds("data/kfm.rds") |> rcopy
kfm |> schema
┌────────────┬───────────────┬──────────────────────────────────┐
│ names      │ scitypes      │ types                            │
├────────────┼───────────────┼──────────────────────────────────┤
│ no         │ Count         │ Int64                            │
│ dl_milk    │ Continuous    │ Float64                          │
│ sex        │ Multiclass{2} │ CategoricalValue{String, UInt32} │
│ weight     │ Continuous    │ Float64                          │
│ ml_suppl   │ Count         │ Int64                            │
│ mat_weight │ Count         │ Int64                            │
│ mat_height │ Count         │ Int64                            │
└────────────┴───────────────┴──────────────────────────────────┘

Data on reported cases of influenza by age group in the 1957 pandemic in England and Wales.

flu = DataFrame(CSV.File("data/fluraw.csv"))
flu |> schema
┌───────┬────────────────┬───────┐
│ names │ scitypes       │ types │
├───────┼────────────────┼───────┤
│ week  │ ScientificDate │ Date  │
│ child │ Count          │ Int64 │
│ young │ Count          │ Int64 │
│ mid   │ Count          │ Int64 │
│ old   │ Count          │ Int64 │
└───────┴────────────────┴───────┘

Data on birth weights from newborns in a London Hospital.

birth = read_rds("data/birthwt.rds") |> rcopy
birth |> schema
┌───────┬───────────────┬──────────────────────────────────┐
│ names │ scitypes      │ types                            │
├───────┼───────────────┼──────────────────────────────────┤
│ low   │ Multiclass{2} │ CategoricalValue{String, UInt32} │
│ age   │ Count         │ Int64                            │
│ lwt   │ Continuous    │ Float64                          │
│ race  │ Multiclass{3} │ CategoricalValue{String, UInt32} │
│ smoke │ Multiclass{2} │ CategoricalValue{String, UInt32} │
│ ptl   │ Count         │ Int64                            │
│ ht    │ Multiclass{2} │ CategoricalValue{String, UInt32} │
│ ui    │ Multiclass{2} │ CategoricalValue{String, UInt32} │
│ ftv   │ Count         │ Int64                            │
│ bwt   │ Count         │ Int64                            │
│ Race  │ Multiclass{2} │ CategoricalValue{String, UInt32} │
└───────┴───────────────┴──────────────────────────────────┘

Data on the energy expenditure in groups of lean and obese women.

energy = rcopy(R"ISwR::energy")
energy |> schema
┌─────────┬───────────────┬──────────────────────────────────┐
│ names   │ scitypes      │ types                            │
├─────────┼───────────────┼──────────────────────────────────┤
│ expend  │ Continuous    │ Float64                          │
│ stature │ Multiclass{2} │ CategoricalValue{String, UInt32} │
└─────────┴───────────────┴──────────────────────────────────┘

Fisher’s iris dataset on measurements for three species of iris.

iris = rcopy(R"datasets::iris")
iris |> schema
┌──────────────┬───────────────┬──────────────────────────────────┐
│ names        │ scitypes      │ types                            │
├──────────────┼───────────────┼──────────────────────────────────┤
│ Sepal_Length │ Continuous    │ Float64                          │
│ Sepal_Width  │ Continuous    │ Float64                          │
│ Petal_Length │ Continuous    │ Float64                          │
│ Petal_Width  │ Continuous    │ Float64                          │
│ Species      │ Multiclass{3} │ CategoricalValue{String, UInt32} │
└──────────────┴───────────────┴──────────────────────────────────┘

3 Distributions

3.1 Histograms

We use histograms to look at the distribution of continuous variables. Histograms make most sense for relatively large data (\(\geq 100\) observations). In this fist histogram, we show the density.

plot(
  birth,
  x = :bwt, Guide.xlabel("Birth weight (g)"),
  Guide.ylabel("Density"),
  Geom.histogram(bincount=30, density=true)
)
Birth weight (g) 0 1000 2000 3000 4000 5000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800 820 840 860 880 900 920 940 960 980 1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200 1220 1240 1260 1280 1300 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 2120 2140 2160 2180 2200 2220 2240 2260 2280 2300 2320 2340 2360 2380 2400 2420 2440 2460 2480 2500 2520 2540 2560 2580 2600 2620 2640 2660 2680 2700 2720 2740 2760 2780 2800 2820 2840 2860 2880 2900 2920 2940 2960 2980 3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200 3220 3240 3260 3280 3300 3320 3340 3360 3380 3400 3420 3440 3460 3480 3500 3520 3540 3560 3580 3600 3620 3640 3660 3680 3700 3720 3740 3760 3780 3800 3820 3840 3860 3880 3900 3920 3940 3960 3980 4000 4020 4040 4060 4080 4100 4120 4140 4160 4180 4200 4220 4240 4260 4280 4300 4320 4340 4360 4380 4400 4420 4440 4460 4480 4500 4520 4540 4560 4580 4600 4620 4640 4660 4680 4700 4720 4740 4760 4780 4800 4820 4840 4860 4880 4900 4920 4940 4960 4980 5000 0 5000 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.000000 0.000025 0.000050 0.000075 0.000100 0.000125 0.000150 0.000175 0.000200 0.000225 0.000250 0.000275 0.000300 0.000325 0.000350 0.000375 0.000400 0.000425 0.000450 0.000475 0.000500 0.000525 0.000550 0.000575 0.000600 0.000000 0.000002 0.000004 0.000006 0.000008 0.000010 0.000012 0.000014 0.000016 0.000018 0.000020 0.000022 0.000024 0.000026 0.000028 0.000030 0.000032 0.000034 0.000036 0.000038 0.000040 0.000042 0.000044 0.000046 0.000048 0.000050 0.000052 0.000054 0.000056 0.000058 0.000060 0.000062 0.000064 0.000066 0.000068 0.000070 0.000072 0.000074 0.000076 0.000078 0.000080 0.000082 0.000084 0.000086 0.000088 0.000090 0.000092 0.000094 0.000096 0.000098 0.000100 0.000102 0.000104 0.000106 0.000108 0.000110 0.000112 0.000114 0.000116 0.000118 0.000120 0.000122 0.000124 0.000126 0.000128 0.000130 0.000132 0.000134 0.000136 0.000138 0.000140 0.000142 0.000144 0.000146 0.000148 0.000150 0.000152 0.000154 0.000156 0.000158 0.000160 0.000162 0.000164 0.000166 0.000168 0.000170 0.000172 0.000174 0.000176 0.000178 0.000180 0.000182 0.000184 0.000186 0.000188 0.000190 0.000192 0.000194 0.000196 0.000198 0.000200 0.000202 0.000204 0.000206 0.000208 0.000210 0.000212 0.000214 0.000216 0.000218 0.000220 0.000222 0.000224 0.000226 0.000228 0.000230 0.000232 0.000234 0.000236 0.000238 0.000240 0.000242 0.000244 0.000246 0.000248 0.000250 0.000252 0.000254 0.000256 0.000258 0.000260 0.000262 0.000264 0.000266 0.000268 0.000270 0.000272 0.000274 0.000276 0.000278 0.000280 0.000282 0.000284 0.000286 0.000288 0.000290 0.000292 0.000294 0.000296 0.000298 0.000300 0.000302 0.000304 0.000306 0.000308 0.000310 0.000312 0.000314 0.000316 0.000318 0.000320 0.000322 0.000324 0.000326 0.000328 0.000330 0.000332 0.000334 0.000336 0.000338 0.000340 0.000342 0.000344 0.000346 0.000348 0.000350 0.000352 0.000354 0.000356 0.000358 0.000360 0.000362 0.000364 0.000366 0.000368 0.000370 0.000372 0.000374 0.000376 0.000378 0.000380 0.000382 0.000384 0.000386 0.000388 0.000390 0.000392 0.000394 0.000396 0.000398 0.000400 0.000402 0.000404 0.000406 0.000408 0.000410 0.000412 0.000414 0.000416 0.000418 0.000420 0.000422 0.000424 0.000426 0.000428 0.000430 0.000432 0.000434 0.000436 0.000438 0.000440 0.000442 0.000444 0.000446 0.000448 0.000450 0.000452 0.000454 0.000456 0.000458 0.000460 0.000462 0.000464 0.000466 0.000468 0.000470 0.000472 0.000474 0.000476 0.000478 0.000480 0.000482 0.000484 0.000486 0.000488 0.000490 0.000492 0.000494 0.000496 0.000498 0.000500 0.000502 0.000504 0.000506 0.000508 0.000510 0.000512 0.000514 0.000516 0.000518 0.000520 0.000522 0.000524 0.000526 0.000528 0.000530 0.000532 0.000534 0.000536 0.000538 0.000540 0.000542 0.000544 0.000546 0.000548 0.000550 0.000552 0.000554 0.000556 0.000558 0.000560 0.000562 0.000564 0.000566 0.000568 0.000570 0.000572 0.000574 0.000576 0.000578 0.000580 0.000582 0.000584 0.000586 0.000588 0.000590 0.000592 0.000594 0.000596 0.000598 0.000600 0.000602 0.000 0.001 Density
Figure 1: Distribution of birth weight from newborns in a London Hospital.

The default for histograms is to show the absolute frequency (counts):

plot(
  wcgs,
  x = :sbp, 
  Geom.histogram(bincount=30),
  Guide.xlabel("SBP (mm Hg)"),
  Guide.ylabel("Counts"),
  Coord.cartesian(xmin=80, ymax=700)
)
SBP (mm Hg) 0 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 0 250 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0 100 200 300 400 500 600 700 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 0 1000 Counts
Figure 2: Distribution of systolic blood pressure (SBP) from subjects in the WCGS dataset.

We can compare distributions using the density or the probability density function (pdf), as shown here:

plot(
  wcgs,
  x = :sbp, xgroup = :chd,
  Geom.subplot_grid(
    Geom.histogram(bincount=30, density=true)
    ),
  Guide.xlabel("SBP (mm Hg)"),
  Guide.ylabel("Density")
)
SBP (mm Hg) CHD No CHD 0 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 0 250 0 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 0 250 0.00 0.01 0.02 0.03 0.04 0.05 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.022 0.024 0.026 0.028 0.030 0.032 0.034 0.036 0.038 0.040 0.042 0.044 0.046 0.048 0.050 0.052 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 0.0026 0.0028 0.0030 0.0032 0.0034 0.0036 0.0038 0.0040 0.0042 0.0044 0.0046 0.0048 0.0050 0.0052 0.0054 0.0056 0.0058 0.0060 0.0062 0.0064 0.0066 0.0068 0.0070 0.0072 0.0074 0.0076 0.0078 0.0080 0.0082 0.0084 0.0086 0.0088 0.0090 0.0092 0.0094 0.0096 0.0098 0.0100 0.0102 0.0104 0.0106 0.0108 0.0110 0.0112 0.0114 0.0116 0.0118 0.0120 0.0122 0.0124 0.0126 0.0128 0.0130 0.0132 0.0134 0.0136 0.0138 0.0140 0.0142 0.0144 0.0146 0.0148 0.0150 0.0152 0.0154 0.0156 0.0158 0.0160 0.0162 0.0164 0.0166 0.0168 0.0170 0.0172 0.0174 0.0176 0.0178 0.0180 0.0182 0.0184 0.0186 0.0188 0.0190 0.0192 0.0194 0.0196 0.0198 0.0200 0.0202 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0226 0.0228 0.0230 0.0232 0.0234 0.0236 0.0238 0.0240 0.0242 0.0244 0.0246 0.0248 0.0250 0.0252 0.0254 0.0256 0.0258 0.0260 0.0262 0.0264 0.0266 0.0268 0.0270 0.0272 0.0274 0.0276 0.0278 0.0280 0.0282 0.0284 0.0286 0.0288 0.0290 0.0292 0.0294 0.0296 0.0298 0.0300 0.0302 0.0304 0.0306 0.0308 0.0310 0.0312 0.0314 0.0316 0.0318 0.0320 0.0322 0.0324 0.0326 0.0328 0.0330 0.0332 0.0334 0.0336 0.0338 0.0340 0.0342 0.0344 0.0346 0.0348 0.0350 0.0352 0.0354 0.0356 0.0358 0.0360 0.0362 0.0364 0.0366 0.0368 0.0370 0.0372 0.0374 0.0376 0.0378 0.0380 0.0382 0.0384 0.0386 0.0388 0.0390 0.0392 0.0394 0.0396 0.0398 0.0400 0.0402 0.0404 0.0406 0.0408 0.0410 0.0412 0.0414 0.0416 0.0418 0.0420 0.0422 0.0424 0.0426 0.0428 0.0430 0.0432 0.0434 0.0436 0.0438 0.0440 0.0442 0.0444 0.0446 0.0448 0.0450 0.0452 0.0454 0.0456 0.0458 0.0460 0.0462 0.0464 0.0466 0.0468 0.0470 0.0472 0.0474 0.0476 0.0478 0.0480 0.0482 0.0484 0.0486 0.0488 0.0490 0.0492 0.0494 0.0496 0.0498 0.0500 0.0502 0.00 0.05 Density
Figure 3: Comparison of systolic blood pressure (SBP) distributions by coronary heart disease (CHD) events.

3.2 Density Plots

Another way to look at the distribution of a continuous variable is with density plots.

plot(
  wcgs,
  x = :sbp, color = :chd,
  Geom.density,
  Guide.xlabel("SBP (mm Hg)"),
  Guide.ylabel("Density"),
  Guide.colorkey(title="CHD"),
  style(line_width=1mm),
  Coord.cartesian(xmin=80)
)
SBP (mm Hg) 0 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 0 250 No CHD CHD CHD h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0.00 0.01 0.02 0.03 0.04 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.022 0.024 0.026 0.028 0.030 0.032 0.034 0.036 0.038 0.040 0.042 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 0.0026 0.0028 0.0030 0.0032 0.0034 0.0036 0.0038 0.0040 0.0042 0.0044 0.0046 0.0048 0.0050 0.0052 0.0054 0.0056 0.0058 0.0060 0.0062 0.0064 0.0066 0.0068 0.0070 0.0072 0.0074 0.0076 0.0078 0.0080 0.0082 0.0084 0.0086 0.0088 0.0090 0.0092 0.0094 0.0096 0.0098 0.0100 0.0102 0.0104 0.0106 0.0108 0.0110 0.0112 0.0114 0.0116 0.0118 0.0120 0.0122 0.0124 0.0126 0.0128 0.0130 0.0132 0.0134 0.0136 0.0138 0.0140 0.0142 0.0144 0.0146 0.0148 0.0150 0.0152 0.0154 0.0156 0.0158 0.0160 0.0162 0.0164 0.0166 0.0168 0.0170 0.0172 0.0174 0.0176 0.0178 0.0180 0.0182 0.0184 0.0186 0.0188 0.0190 0.0192 0.0194 0.0196 0.0198 0.0200 0.0202 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0226 0.0228 0.0230 0.0232 0.0234 0.0236 0.0238 0.0240 0.0242 0.0244 0.0246 0.0248 0.0250 0.0252 0.0254 0.0256 0.0258 0.0260 0.0262 0.0264 0.0266 0.0268 0.0270 0.0272 0.0274 0.0276 0.0278 0.0280 0.0282 0.0284 0.0286 0.0288 0.0290 0.0292 0.0294 0.0296 0.0298 0.0300 0.0302 0.0304 0.0306 0.0308 0.0310 0.0312 0.0314 0.0316 0.0318 0.0320 0.0322 0.0324 0.0326 0.0328 0.0330 0.0332 0.0334 0.0336 0.0338 0.0340 0.0342 0.0344 0.0346 0.0348 0.0350 0.0352 0.0354 0.0356 0.0358 0.0360 0.0362 0.0364 0.0366 0.0368 0.0370 0.0372 0.0374 0.0376 0.0378 0.0380 0.0382 0.0384 0.0386 0.0388 0.0390 0.0392 0.0394 0.0396 0.0398 0.0400 0.0402 0.00 0.05 Density
Figure 4: Distribution of systolic blood pressure (SBP) by coronary heart disease (CHD) event.

Diastolic blood pressure (DBP) is skewed to the right (see the QQ-Plot). In the following example, we log-transform DBP.

plot(
  wcgs,
  x = log.(wcgs.dbp), color = :chd,
  Geom.density,
  Guide.xlabel("log (DBP)"),
  Guide.ylabel("Density"),
  Guide.colorkey(title="CHD"),
  style(line_width=1mm),
)
log (DBP) 3.9 4.2 4.5 4.8 5.1 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00 5.05 5.10 3.900 3.905 3.910 3.915 3.920 3.925 3.930 3.935 3.940 3.945 3.950 3.955 3.960 3.965 3.970 3.975 3.980 3.985 3.990 3.995 4.000 4.005 4.010 4.015 4.020 4.025 4.030 4.035 4.040 4.045 4.050 4.055 4.060 4.065 4.070 4.075 4.080 4.085 4.090 4.095 4.100 4.105 4.110 4.115 4.120 4.125 4.130 4.135 4.140 4.145 4.150 4.155 4.160 4.165 4.170 4.175 4.180 4.185 4.190 4.195 4.200 4.205 4.210 4.215 4.220 4.225 4.230 4.235 4.240 4.245 4.250 4.255 4.260 4.265 4.270 4.275 4.280 4.285 4.290 4.295 4.300 4.305 4.310 4.315 4.320 4.325 4.330 4.335 4.340 4.345 4.350 4.355 4.360 4.365 4.370 4.375 4.380 4.385 4.390 4.395 4.400 4.405 4.410 4.415 4.420 4.425 4.430 4.435 4.440 4.445 4.450 4.455 4.460 4.465 4.470 4.475 4.480 4.485 4.490 4.495 4.500 4.505 4.510 4.515 4.520 4.525 4.530 4.535 4.540 4.545 4.550 4.555 4.560 4.565 4.570 4.575 4.580 4.585 4.590 4.595 4.600 4.605 4.610 4.615 4.620 4.625 4.630 4.635 4.640 4.645 4.650 4.655 4.660 4.665 4.670 4.675 4.680 4.685 4.690 4.695 4.700 4.705 4.710 4.715 4.720 4.725 4.730 4.735 4.740 4.745 4.750 4.755 4.760 4.765 4.770 4.775 4.780 4.785 4.790 4.795 4.800 4.805 4.810 4.815 4.820 4.825 4.830 4.835 4.840 4.845 4.850 4.855 4.860 4.865 4.870 4.875 4.880 4.885 4.890 4.895 4.900 4.905 4.910 4.915 4.920 4.925 4.930 4.935 4.940 4.945 4.950 4.955 4.960 4.965 4.970 4.975 4.980 4.985 4.990 4.995 5.000 5.005 5.010 5.015 5.020 5.025 5.030 5.035 5.040 5.045 5.050 5.055 5.060 5.065 5.070 5.075 5.080 5.085 5.090 5.095 5.100 5.105 3.9 4.2 4.5 4.8 5.1 No CHD CHD CHD h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0 1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00 2.02 2.04 2.06 2.08 2.10 2.12 2.14 2.16 2.18 2.20 2.22 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38 2.40 2.42 2.44 2.46 2.48 2.50 2.52 2.54 2.56 2.58 2.60 2.62 2.64 2.66 2.68 2.70 2.72 2.74 2.76 2.78 2.80 2.82 2.84 2.86 2.88 2.90 2.92 2.94 2.96 2.98 3.00 3.02 3.04 3.06 3.08 3.10 3.12 3.14 3.16 3.18 3.20 3.22 3.24 3.26 3.28 3.30 3.32 3.34 3.36 3.38 3.40 3.42 3.44 3.46 3.48 3.50 3.52 3.54 3.56 3.58 3.60 3.62 3.64 3.66 3.68 3.70 3.72 3.74 3.76 3.78 3.80 3.82 3.84 3.86 3.88 3.90 3.92 3.94 3.96 3.98 4.00 4.02 4.04 4.06 4.08 4.10 4.12 4.14 4.16 4.18 4.20 4.22 4.24 4.26 4.28 4.30 4.32 4.34 4.36 4.38 4.40 4.42 4.44 4.46 4.48 4.50 4.52 4.54 4.56 4.58 4.60 4.62 4.64 4.66 4.68 4.70 4.72 4.74 4.76 4.78 4.80 4.82 4.84 4.86 4.88 4.90 4.92 4.94 4.96 4.98 5.00 0 5 Density
Figure 5: Comparison of diastolic blood pressure (DBP) distributions between coronary heart disease (CHD) status of the subjects. DBP was log-transformed to bring it closer to a normal distribution.
Tip

We have missing values in chol, thus we need to drop them before constructing a density plot or else, we would have an error.

plot(
  @subset(wcgs, !ismissing(:chol)),
  x = :chol, color = :chd,
  Geom.density,
  Guide.xlabel("Cholesterol (mg/dl)"),
  Guide.ylabel("Density"),
  Guide.colorkey(title="CHD"),
  style(line_width=1mm),
  Coord.cartesian(ymax=0.011)
)
Cholesterol (mg/dl) 0 200 400 600 800 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 0 1000 No CHD CHD CHD h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0.000 0.005 0.010 0.015 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040 0.0045 0.0050 0.0055 0.0060 0.0065 0.0070 0.0075 0.0080 0.0085 0.0090 0.0095 0.0100 0.0105 0.0110 0.00000 0.00005 0.00010 0.00015 0.00020 0.00025 0.00030 0.00035 0.00040 0.00045 0.00050 0.00055 0.00060 0.00065 0.00070 0.00075 0.00080 0.00085 0.00090 0.00095 0.00100 0.00105 0.00110 0.00115 0.00120 0.00125 0.00130 0.00135 0.00140 0.00145 0.00150 0.00155 0.00160 0.00165 0.00170 0.00175 0.00180 0.00185 0.00190 0.00195 0.00200 0.00205 0.00210 0.00215 0.00220 0.00225 0.00230 0.00235 0.00240 0.00245 0.00250 0.00255 0.00260 0.00265 0.00270 0.00275 0.00280 0.00285 0.00290 0.00295 0.00300 0.00305 0.00310 0.00315 0.00320 0.00325 0.00330 0.00335 0.00340 0.00345 0.00350 0.00355 0.00360 0.00365 0.00370 0.00375 0.00380 0.00385 0.00390 0.00395 0.00400 0.00405 0.00410 0.00415 0.00420 0.00425 0.00430 0.00435 0.00440 0.00445 0.00450 0.00455 0.00460 0.00465 0.00470 0.00475 0.00480 0.00485 0.00490 0.00495 0.00500 0.00505 0.00510 0.00515 0.00520 0.00525 0.00530 0.00535 0.00540 0.00545 0.00550 0.00555 0.00560 0.00565 0.00570 0.00575 0.00580 0.00585 0.00590 0.00595 0.00600 0.00605 0.00610 0.00615 0.00620 0.00625 0.00630 0.00635 0.00640 0.00645 0.00650 0.00655 0.00660 0.00665 0.00670 0.00675 0.00680 0.00685 0.00690 0.00695 0.00700 0.00705 0.00710 0.00715 0.00720 0.00725 0.00730 0.00735 0.00740 0.00745 0.00750 0.00755 0.00760 0.00765 0.00770 0.00775 0.00780 0.00785 0.00790 0.00795 0.00800 0.00805 0.00810 0.00815 0.00820 0.00825 0.00830 0.00835 0.00840 0.00845 0.00850 0.00855 0.00860 0.00865 0.00870 0.00875 0.00880 0.00885 0.00890 0.00895 0.00900 0.00905 0.00910 0.00915 0.00920 0.00925 0.00930 0.00935 0.00940 0.00945 0.00950 0.00955 0.00960 0.00965 0.00970 0.00975 0.00980 0.00985 0.00990 0.00995 0.01000 0.01005 0.01010 0.01015 0.01020 0.01025 0.01030 0.01035 0.01040 0.01045 0.01050 0.01055 0.01060 0.01065 0.01070 0.01075 0.01080 0.01085 0.01090 0.01095 0.01100 0.00 0.02 Density
Figure 6: Distribution of blood cholesterol by coronary heart disease (CHD) event from the WCGS dataset.

3.3 QQ-Plots

The best way to determine if a continuous variable is normally distributed or not is with quantile-quantile plots (QQ-plots). We plot the quantiles of our variable of interest against quantiles from the standard normal distribution (which has a mean \(\mu=0\) and a standard deviation \(\sigma=1\)). This type of QQ-plots against the normal distribution are known as QQ-normal plots. If the variable is normally distributed, then a linear relationship will be observed.

qq_plot(birth.bwt; ylab = "Birth weight (g)")
Theoretical quantiles 0 1000 2000 3000 4000 5000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800 820 840 860 880 900 920 940 960 980 1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200 1220 1240 1260 1280 1300 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 2120 2140 2160 2180 2200 2220 2240 2260 2280 2300 2320 2340 2360 2380 2400 2420 2440 2460 2480 2500 2520 2540 2560 2580 2600 2620 2640 2660 2680 2700 2720 2740 2760 2780 2800 2820 2840 2860 2880 2900 2920 2940 2960 2980 3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200 3220 3240 3260 3280 3300 3320 3340 3360 3380 3400 3420 3440 3460 3480 3500 3520 3540 3560 3580 3600 3620 3640 3660 3680 3700 3720 3740 3760 3780 3800 3820 3840 3860 3880 3900 3920 3940 3960 3980 4000 4020 4040 4060 4080 4100 4120 4140 4160 4180 4200 4220 4240 4260 4280 4300 4320 4340 4360 4380 4400 4420 4440 4460 4480 4500 4520 4540 4560 4580 4600 4620 4640 4660 4680 4700 4720 4740 4760 4780 4800 4820 4840 4860 4880 4900 4920 4940 4960 4980 5000 0 5000 4972.8048352021964792.55026455026 4698.66368763849554418.317460317459 4558.7664228242314206.846560846561 4461.2301160850234170.62962962963 4385.1540512618674160.333333333333 4322.1918025565314133.222222222223 4268.12672391513754084.460317460318 4220.5187761918254054.0 4177.8235863833514028.063492063492 4138.99911201847953997.0 4103.30762326136853990.777777777778 4070.2068677406883976.8518518518517 4039.28608754003933956.851851851852 4010.22634148704133941.0 3982.7748070077043940.5767195767194 3956.72752431161233928.296296296296 3931.91745071013973900.4444444444443 3908.2059722377183884.0 3885.47673400564743874.3492063492067 3863.6310662813643860.0 3842.58453384706633858.4338624338625 3822.2642920499693844.7989417989415 3802.60703260832543816.333333333333 3783.557367528373795.6190476190477 3765.0665432108783782.5925925925926 3747.0914066888463770.0 3729.5935667003983770.0 3712.5387069727333765.0370370370365 3695.89601961515473746.222222222222 3679.6377341689223718.026455026455 3663.73872349300433682.7460317460327 3648.17617185858853651.0 3632.92929378201553651.0 3617.9790945258873651.0 3603.30816503979533648.460317460317 3588.9005055377513641.126984126984 3574.74137302180223634.544973544974 3560.81714893615073629.0 3547.1152238288253624.555555555555 3533.62389645037233614.0 3520.3322851622713610.0 3507.2302498856023596.074074074074 3494.30832311099863582.148148148148 3481.5576487280493572.0 3468.96992762686573564.592592592593 3456.53736918495863544.0 3444.25264788539333529.5238095238096 3432.10886442278343483.5185185185187 3420.09951074598083469.8359788359785 3408.2184385638433459.761904761905 3396.4598309056463455.507936507937 3384.81817638288753440.814814814815 3373.28824584595583426.8888888888887 3361.86507116896753412.9629629629635 3350.54392593002473396.074074074074 3339.3203077832773374.0 3328.18992234413553365.354497354497 3317.14866843055553329.042328042328 3306.1926245218723320.2380952380954 3295.31803631281763317.0 3284.5213052543123317.0 3273.79897798481533314.5555555555557 3263.147736566643298.089947089947 3252.56438945093263274.0 3242.04586310314433271.7777777777774 3231.5891942280043256.0105820105828 3221.19152253925043233.7037037037035 3210.8500840249743232.0 3200.5622046642763231.037037037037 3190.3252945553223225.0 3180.1368424186773222.206349206349 3169.9944104432453203.0 3159.89562944514143203.0 3149.83819431254323199.888888888889 3139.8198597119463175.0 3129.83843603341443172.1851851851857 3119.8917855543123145.5714285714284 3109.97781880272033129.4814814814818 3100.0944911032673103.6613756613756 3090.23979928946353099.2063492063494 3080.41177856786633090.0 3070.6084995204773090.0 3060.8280652327513089.365079365079 3051.06860853549373078.952380952381 3041.3282893496523062.0 3031.60529212374973062.0 3021.89782335428753062.0 3012.20410917999333062.0 3002.52239304127763061.365079365079 2992.85093339666453041.7619047619046 2983.18800148832773032.4074074074074 2973.5318791491673004.5555555555557 2963.8808566441232977.0 2954.2332305386342977.0 2944.58730158730172977.0 2934.94137263596942977.0 2925.29374653048032948.3068783068784 2915.64272402543662948.0 2905.98660168627572922.5502645502647 2896.3236697779392920.0529100529097 2886.65221013332582920.0 2876.970493994612920.0 2867.2767798203162920.0 2857.56931105085372906.6666666666665 2847.84631382495132878.5343915343915 2838.10599463910972877.0 2828.3465379418522863.888888888889 2818.56610365412642837.8571428571427 2808.7628246067372835.074074074074 2798.93480388514042835.0 2789.08011207133632822.185185185185 2779.1967843718832808.259259259259 2769.28281762029162784.3809523809523 2759.33616714118942778.402116402116 2749.35474346265762769.952380952381 2739.336408862062769.0 2729.2789737294622753.095238095238 2719.1801927313582750.121693121693 2709.03776075592622735.15873015873 2698.8493086192812723.4550264550267 2688.61239851032722672.84126984127 2678.32451914962942663.285714285714 2667.9830806353532640.8518518518517 2657.58540894659972637.0 2647.1287400714592624.3809523809523 2636.6102137236712603.608465608466 2626.02686660796332595.0158730158732 2615.37562518978852563.4603174603176 2604.6532979202912552.0793650793653 2593.85656686178572528.185185185185 2582.98197865273142500.333333333333 2572.0259347440482495.0 2560.9846808304682495.0 2549.85429539132662495.0 2538.63067724457872472.137566137566 2527.3095320056362466.0 2515.88635732864762466.0 2504.3564267917162453.6402116402114 2492.71477226895742443.862433862434 2480.95616461076042438.9523809523807 2469.07509242862262427.4074074074074 2457.06573875182042416.4867724867727 2444.921955289212411.0158730158732 2432.63723398964482410.0 2420.20467554773772410.0 2407.61695444655422388.8253968253966 2394.8662800636052381.0 2381.94435328900142381.0 2368.84231801233232371.0 2355.5507067242312357.074074074074 2342.05937934577832353.0 2328.35745423845262333.4444444444443 2314.4332301528012308.3650793650795 2300.27409763685232297.5608465608466 2285.8664381348082296.0 2271.19550864871642286.5185185185182 2256.2453093925882253.777777777778 2240.9984313160152240.0 2225.4358796815992230.079365079365 2209.5368690056812215.814814814815 2193.27858355944862195.3809523809523 2176.63589620187032187.0 2159.58103647420562147.9470899470903 2142.08319648575752125.3650793650795 2124.10805996372532109.259259259259 2105.61723564623342090.010582010582 2086.5675705662782084.0 2066.91031112463452082.772486772487 2046.5900693275372065.5714285714284 2025.54353689323972055.0 2003.6978691689562004.179894179894 1980.96863093688561949.851851851852 1957.25715246446361931.3015873015875 1932.4470788629911928.0 1906.3997961668991928.0 1878.94826168756191911.4285714285716 1849.88851563456431895.6031746031747 1818.96773543391551888.5132275132275 1785.86697991323511847.7777777777778 1750.1754911561241802.5925925925926 1711.35101679125251756.756613756614 1668.65582698277851713.888888888889 1621.04787925946581640.6137566137565 1566.9828006180731588.0 1504.02055191273641528.2857142857142 1427.94448708958071399.3333333333335 1330.4081803503721229.9206349206347 1190.51091553610851077.095238095238 916.3697679724055864.1746031746031 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0 1000 2000 3000 4000 5000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 4200 4400 4600 4800 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800 820 840 860 880 900 920 940 960 980 1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200 1220 1240 1260 1280 1300 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 2120 2140 2160 2180 2200 2220 2240 2260 2280 2300 2320 2340 2360 2380 2400 2420 2440 2460 2480 2500 2520 2540 2560 2580 2600 2620 2640 2660 2680 2700 2720 2740 2760 2780 2800 2820 2840 2860 2880 2900 2920 2940 2960 2980 3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200 3220 3240 3260 3280 3300 3320 3340 3360 3380 3400 3420 3440 3460 3480 3500 3520 3540 3560 3580 3600 3620 3640 3660 3680 3700 3720 3740 3760 3780 3800 3820 3840 3860 3880 3900 3920 3940 3960 3980 4000 4020 4040 4060 4080 4100 4120 4140 4160 4180 4200 4220 4240 4260 4280 4300 4320 4340 4360 4380 4400 4420 4440 4460 4480 4500 4520 4540 4560 4580 4600 4620 4640 4660 4680 4700 4720 4740 4760 4780 4800 0 5000 Birth weight (g)
Figure 7: QQ-plot of birth weights from newborns in a London hospital.
Note

The function qq_plot is part of pubh.jl, a wrapper to functions from Gadfly constructs QQ-plots.

Right-skewed variables, show an upper right curve in the QQ-plot:

qq_plot(wcgs.dbp; ylab="DBP (mm Hg)")
Theoretical quantiles 0 50 100 150 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5 51.0 51.5 52.0 52.5 53.0 53.5 54.0 54.5 55.0 55.5 56.0 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0 60.5 61.0 61.5 62.0 62.5 63.0 63.5 64.0 64.5 65.0 65.5 66.0 66.5 67.0 67.5 68.0 68.5 69.0 69.5 70.0 70.5 71.0 71.5 72.0 72.5 73.0 73.5 74.0 74.5 75.0 75.5 76.0 76.5 77.0 77.5 78.0 78.5 79.0 79.5 80.0 80.5 81.0 81.5 82.0 82.5 83.0 83.5 84.0 84.5 85.0 85.5 86.0 86.5 87.0 87.5 88.0 88.5 89.0 89.5 90.0 90.5 91.0 91.5 92.0 92.5 93.0 93.5 94.0 94.5 95.0 95.5 96.0 96.5 97.0 97.5 98.0 98.5 99.0 99.5 100.0 100.5 101.0 101.5 102.0 102.5 103.0 103.5 104.0 104.5 105.0 105.5 106.0 106.5 107.0 107.5 108.0 108.5 109.0 109.5 110.0 110.5 111.0 111.5 112.0 112.5 113.0 113.5 114.0 114.5 115.0 115.5 116.0 116.5 117.0 117.5 118.0 118.5 119.0 119.5 120.0 120.5 121.0 121.5 122.0 122.5 123.0 123.5 124.0 124.5 125.0 125.5 126.0 126.5 127.0 127.5 128.0 128.5 129.0 129.5 130.0 130.5 131.0 131.5 132.0 132.5 133.0 133.5 134.0 134.5 135.0 135.5 136.0 136.5 137.0 137.5 138.0 138.5 139.0 139.5 140.0 140.5 141.0 141.5 142.0 142.5 143.0 143.5 144.0 144.5 145.0 145.5 146.0 146.5 147.0 147.5 148.0 148.5 149.0 149.5 150.0 0 200 117.03598148179549143.00221940393294 114.15373570708542133.00285351933962 112.73398858366959129.5007926442613 111.76713857450513127.00443880786224 111.0271157921894124.50142675967027 110.42451844894643124.0 109.91451890814444123.00412175015845 109.47133853828521122.0 109.07874929594958121.00538998097636 108.7258539784001120.0 108.40497112187973120.0 108.11047700594257119.00729232720369 107.83812727416232118.0 107.58463760777131118.0 107.34741294995081117.00919467343101 107.12436619084718116.0 106.9137929761428116.0 106.71428296716843116.0 106.52465549190225116.0 106.3439119448645115.01236525047534 106.17119995259237114.0 106.00578597192685114.0 105.84703404168121114.0 105.69438909716348114.0 105.54736371757288114.0 105.40552749032052113.01616994292999 105.26849839431637112.0 105.13593575806742112.0 105.0075344585771112.0 104.88302010699346112.0 104.76214502573812111.01934051997432 104.6446848655626110.0 104.53043574384425110.0 104.41921181038988110.0 104.31084316613932110.0 104.20517407494958110.0 104.10206142016425110.0 104.00137336672667110.0 103.90298819675597110.0 103.80679329220861110.0 103.71268424282128110.0 103.62056406121691110.0 103.53034249004688110.0 103.44193538848009110.0 103.35526418734963110.0 103.27025540391324110.0 103.1868402085466110.0 103.10495403682086110.0 103.02453624136143110.0 102.94552977867733109.03138871274587 102.86788092681624108.0 102.79153903026507108.0 102.71645626899101108.0 102.64258744892521108.0 102.56988981153661108.0 102.49832286043997108.0 102.4278482032365108.0 102.358429407004108.0 102.29003186604305108.0 102.2226226806488108.0 102.15617054582034108.0 102.09064564894267108.0 102.02601957558467107.03963221306276 101.9622652226502106.0 101.89935671820177106.0 101.83726934734958106.0 101.7759794836613106.0 101.71546452560534106.0 101.6557028375887106.0 101.59667369519612106.0 101.53835723427451106.0 101.48073440354261106.0 101.42378692043572106.0 101.36749722992342106.0 101.31184846606264106.0 101.25682441606985106.0 101.20240948671655105.52425491439453 101.14858867286944104.52457197209878 101.09534752801252104.0 101.04267213660268104.0 100.99054908812303104.0 100.9389654527105104.0 100.8879087582433104.0 100.83736696878486104.0 100.78732846428842104.0 100.73778202147457104.0 100.6887167958011104.0 100.64012230445066104.0 100.59198841026839104.0 100.54430530658558104.0 100.49706350287191104.0 100.4502538111617104.0 100.40386733320514104.0 100.35789544829773104.0 100.31232980174559104.0 100.26716229392723104.0 100.22238506991454104.0 100.17799050961935104.0 100.13397121843359104.0 100.09032001833378104.0 100.04702993942223104.0 100.00409421187923104.0 99.96150625830292104.0 99.91925968641407104.0 99.87734828210523103.06626506024077 99.83576600281492102.0 99.79450697120868102.0 99.75356546914978102.0 99.71293593194432102.0 99.67261294284515102.0 99.63259122780124102.0 99.59286565043914102.0 99.55343120726428102.0 99.5142830230709102.0 99.47541634654931102.0 99.43682654608082102.0 99.39850910571045102.0 99.36045962128864102.0 99.32267379677329102.0 99.2851474406844102.0 99.24787646270356102.0 99.21085687041156101.0770450221944 99.17408476615685100.0 99.13755634404926100.0 99.10126788707245100.0 99.06521576430984100.0 99.02939642827835100.0 98.99380641236536100.0 98.95844232836384100.0 98.92330086410107100.0 98.88837878115696100.0 98.85367291266792100.0 98.81918016121207100.0 98.78489749677261100.0 98.7508219547758100.0 98.71695063420006100.0 98.68328069575338100.0 98.64980936011594100.0 98.61653390624515100.0 98.58345166974064100.0 98.55056004126625100.0 98.51785646502724100.0 98.48533843729983100.0 98.45300350501128100.0 98.42084926436826100.0 98.38887335953177100.0 98.35707348133629100.0 98.32544736605189100.0 98.29399279418728100.0 98.2627075893322100.0 98.23158961703768100.0 98.2006367837327100.0 98.16984703567573100.0 98.13921835793991100.0 98.10874877343052100.0 98.07843634193345100.0 98.04827915919385100.0 98.01827535602311100.0 97.98842309743394100.0 97.95872058180188100.0 97.9291660400527100.0 97.89975773487427100.0 97.87049395995254100.0 97.84137303923032100.0 97.81239332618831100.0 97.78355320314749100.0 97.75485108059198100.0 97.72628539651195100.0 97.69785461576558100.0 97.66955722945956100.0 97.64139175434748100.0 97.61335673224538100.0 97.58545072946404100.0 97.55767233625733100.0 97.53002016628601100.0 97.50249285609672100.0 97.475089064615399.1119213696893 97.447807472654298.0 97.4206467824335898.0 97.3936057171152198.0 97.3666830203494498.0 97.3398774558341398.0 97.3131878068856198.0 97.2866128760210498.0 97.26015148455298.0 97.2338024721887698.0 97.2075646966549898.0 97.181437033312598.0 97.15541837479698.0 97.1295076306569698.0 97.1037037270169698.0 97.078005606229898.0 97.0524122265522498.0 97.0269225618231398.0 97.0015356011505598.0 96.9762503486070198.0 96.9510658229320198.0 96.9259810572421598.0 96.9009950987484798.0 96.8761070084805698.0 96.8513158610175798.0 96.8266207442257498.0 96.8020207590022698.0 96.777515019025498.0 96.753102650510598.0 96.728782791971998.0 96.7045545939905598.0 96.6804172189869598.0 96.6563698409996498.0 96.632411645468898.0 96.6085418290248298.0 96.5847595992818898.0 96.561064174636398.0 96.5374547840694598.0 96.5139306669551998.0 96.490491072871898.0 96.4671352614179798.0 96.4438625020331798.0 96.420672073821998.0 96.397563265381998.0 96.3745353746362798.0 96.3515877086691398.0 96.3287195835651298.0 96.3059303242522398.0 96.2832192643482598.0 96.2605857460103898.0 96.2380291197882197.14362714013987 96.2155487444798696.0 96.193143986991296.0 96.1708142221980396.0 96.1485588328112696.0 96.1263772092449596.0 96.1042687494870696.0 96.08223285897396.0 96.0602689504617696.0 96.038376443914796.0 96.0165547663767496.0 95.994803351860196.0 95.9731216412304596.0 95.951509082095296.0 95.9299651286943696.0 95.908489241793496.0 95.8870808885783596.0 95.8657395425529796.0 95.8444646834380896.0 95.8232557970728396.0 95.8021123753178996.0 95.7810339159606896.0 95.7600199226223396.0 95.7390699046666896.0 95.7181833771107296.0 95.6973598605371696.0 95.6765988810084396.0 95.6558999699824496.0 95.6352626642299796.0 95.6146865057536496.0 95.5941710417083696.0 95.5737158243234796.0 95.5533204108260796.0 95.5329843633661596.0 95.5127072489428596.0 95.4924886393321596.0 95.4723281110161396.0 95.452225245113296.0 95.4321796273098896.0 95.4121908477938296.0 95.3922585011878596.0 95.3723821864855296.0 95.3525615069875896.0 95.3327960702397896.0 95.313085487971796.0 95.2934293760367196.0 95.2738273543530296.0 95.2542790468457896.0 95.2347840813902596.0 95.215342089755996.0 95.1959527075515696.0 95.1766155741715496.0 95.1573303327426796.0 95.138096630072396.0 95.1189141165971796.0 95.0997824463332296.0 95.080701276826296.0 95.0616702691032296.0 95.0426890876250696.0 95.0237574002393896.0 95.0048748781345796.0 94.9860411957946396.0 94.9672560309546296.0 94.9485190645568996.0 94.9298299807081596.0 94.9111884666371495.18484464172434 94.8925942126531894.0 94.874046912105194.0 94.8555462613412394.0 94.837091959669894.0 94.818683709320194.0 94.8003212154041794.0 94.782004185879394.0 94.76373233151194.0 94.7455053658365594.0 94.7273230051293494.0 94.7091849683635494.0 94.6910909771794894.0 94.6730407558496694.0 94.6550340312449894.0 94.63707053280294.0 94.619149992490394.0 94.6012721447805494.0 94.5834367266130294.0 94.565643477366794.0 94.5478921388287994.0 94.530182455164694.0 94.5125141728882294.0 94.4948870408332594.0 94.477300810124394.0 94.4597552341488394.0 94.442250068529394.0 94.4247850710959594.0 94.407360001859994.0 94.3899746229865994.0 94.372628698769894.0 94.3553219956058894.0 94.338054281968594.0 94.3208253283837394.0 94.3036349074055494.0 94.2864827935914994.0 94.2693687634790894.0 94.2522925955622494.0 94.2352540702681694.0 94.2182529699346194.0 94.201289078787594.0 94.1843621829187394.0 94.1674720702644794.0 94.1506185305836694.0 94.1338013554369394.0 94.1170203381657294.0 94.1002752738717394.0 94.0835659593967494.0 94.0668921933026594.0 94.050253775851894.0 94.033650508987694.0 94.0170821963154794.0 94.0005486430839794.0 93.9840496561662894.0 93.9675850440418494.0 93.9511546167784494.0 93.9347581860142594.0 93.9183955649404894.0 93.9020665682840194.0 93.8857710122902994.0 93.8695087147066194.0 93.8532794947655293.22352568167389 93.8370831731684292.0 93.8209195720695392.0 93.8047885150599192.0 93.7886898271518792.0 93.7726233347634192.0 93.7565888657030292.0 93.7405862491546392.0 93.7246153156627792.0 93.7086758971179392.0 93.6927678267420692.0 93.6768909390744392.0 93.661045069957592.0 93.6452300565230592.0 93.6294457371785192.0 93.6136919515935192.0 93.5979685406864292.0 93.5822753466113892.0 93.566612212745292.0 93.5509789836745792.0 93.5353755051835192.0 93.5198016242408392.0 93.5042571889878492.0 93.4887420487261892.0 93.4732560539059392.0 93.4577990561136492.0 93.442370908060892.0 93.4269714635721692.0 93.4116005775744592.0 93.3962581060851692.0 93.3809439062013792.0 93.3656578360888492.0 93.3503997549712892.0 93.335169523119592.0 93.3199670018410692.0 93.3047920534697492.0 93.2896445413553392.0 93.2745243298534392.0 93.2594312843155592.0 93.2443652710790692.0 93.2293261574575492.0 93.2143138117310992.0 93.1993281031367992.0 93.1843689018593692.0 93.1694360790217592.0 93.1545295066760792.0 93.1396490577944692.0 93.1247946062601592.0 93.1099660268586792.0 93.0951631952690192.0 93.0803859880550392.0 93.06563428265792.0 93.0509079573830792.0 93.0362068914010292.0 93.0215309647392.0 93.0068800582324592.0 92.9922540536060292.0 92.9776528333756492.0 92.9630762808857792.0 92.9485242802925592.0 92.933996716556292.0 92.9194934754334692.0 92.9050144434701292.0 92.8905595079936192.0 92.8761285571057492.0 92.8617214796754892.0 92.8473381653317992.0 92.8329785044566392.0 92.8186423881779992.0 92.8043297083629792.0 92.7900403576110392.0 92.7757742292472392.0 92.7615312173155992.0 92.7473112165725692.0 92.7331141224804492.0 92.7189398312010892.0 92.704788239589492.0 92.6906592451872592.0 92.6765527462170892.0 92.6624686415759192.0 92.6484068308292392.0 92.6343672142049492.0 92.6203496925875592.0 92.6063541675122492.0 92.5923805411590392.0 92.5784287163471592.0 92.564498596529392.0 92.5505900857860792.0 92.5367030888203991.27932783766664 92.5228375109520390.0 92.5089932581122790.0 92.4951702368384290.0 92.481368354268690.0 92.4675875181364590.0 92.4538276367660190.0 92.4400886190664990.0 92.426370374527390.0 92.4126728132129990.0 92.3989958457582690.0 92.3853393833630990.0 92.3717033377878890.0 92.358087621348690.0 92.3444921469121390.0 92.3309168278914690.0 92.3173615782410890.0 92.3038263124524190.0 92.2903109455492190.0 92.2768153930830690.0 92.2633395711289590.0 92.2498833962808590.0 92.2364467856473590.0 92.2230296568473290.0 92.2096319280056890.0 92.1962535177491690.0 92.1828943452020790.0 92.1695543299822990.0 92.1562333921970190.0 92.1429314524387990.0 92.129648431781590.0 92.1163842517764290.0 92.103138834448290.0 92.0899121022910790.0 92.0767039782649390.0 92.0635143857916290.0 92.0503432487510890.0 92.0371904914775990.0 92.0240560387562190.0 92.0109398158190190.0 91.997841748341590.0 91.9847617624390290.0 91.9716997846632490.0 91.958655741998690.0 91.9456295618589190.0 91.9326211720838390.0 91.9196305009355190.0 91.906657477095290.0 91.8937020296599990.0 91.8807640881393790.0 91.867843582452190.0 91.8549404429228590.0 91.8420546002791190.0 91.8291859856479790.0 91.816334530552990.0 91.8035001669107890.0 91.7906828270287290.0 91.7778824436010790.0 91.7650989497063190.0 91.752332278804290.0 91.739582364732790.0 91.7268491417050690.0 91.7141325443069590.0 91.7014325074935990.0 91.6887489665868490.0 91.6760818572724690.0 91.6634311155972590.0 91.6507966779663390.0 91.6381784811403390.0 91.6255764622328190.0 91.6129905587074290.0 91.6004207083753790.0 91.5878668493926490.0 91.5753289202575690.0 91.5628068598080990.0 91.5503006072192490.0 91.5378101020006690.0 91.5253352839940290.0 91.5128760933705490.0 91.5004324706285290.0 91.4880043565909690.0 91.4755916924030790.0 91.4631944195298490.0 91.450812479753890.0 91.438445815172590.0 91.4260943681963390.0 91.4137580815460990.0 91.4014368982507890.0 91.3891307616452890.0 91.3768396153681490.0 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56.19294438087885660.0 55.9205946490986660.0 55.6261005331614960.0 55.3052176766410960.0 54.95232235909169660.0 54.5597331167560260.0 54.1165527468967660.0 53.606553206094760.0 53.0039558628518760.0 52.2639330805360960.0 51.297083071371558.998414711477494 49.8773359479560658.0 46.9950901732459958.0 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0 50 100 150 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5 51.0 51.5 52.0 52.5 53.0 53.5 54.0 54.5 55.0 55.5 56.0 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0 60.5 61.0 61.5 62.0 62.5 63.0 63.5 64.0 64.5 65.0 65.5 66.0 66.5 67.0 67.5 68.0 68.5 69.0 69.5 70.0 70.5 71.0 71.5 72.0 72.5 73.0 73.5 74.0 74.5 75.0 75.5 76.0 76.5 77.0 77.5 78.0 78.5 79.0 79.5 80.0 80.5 81.0 81.5 82.0 82.5 83.0 83.5 84.0 84.5 85.0 85.5 86.0 86.5 87.0 87.5 88.0 88.5 89.0 89.5 90.0 90.5 91.0 91.5 92.0 92.5 93.0 93.5 94.0 94.5 95.0 95.5 96.0 96.5 97.0 97.5 98.0 98.5 99.0 99.5 100.0 100.5 101.0 101.5 102.0 102.5 103.0 103.5 104.0 104.5 105.0 105.5 106.0 106.5 107.0 107.5 108.0 108.5 109.0 109.5 110.0 110.5 111.0 111.5 112.0 112.5 113.0 113.5 114.0 114.5 115.0 115.5 116.0 116.5 117.0 117.5 118.0 118.5 119.0 119.5 120.0 120.5 121.0 121.5 122.0 122.5 123.0 123.5 124.0 124.5 125.0 125.5 126.0 126.5 127.0 127.5 128.0 128.5 129.0 129.5 130.0 130.5 131.0 131.5 132.0 132.5 133.0 133.5 134.0 134.5 135.0 135.5 136.0 136.5 137.0 137.5 138.0 138.5 139.0 139.5 140.0 140.5 141.0 141.5 142.0 142.5 143.0 143.5 50 100 150 DBP (mm Hg)
Figure 8: QQ-plot of diastolic blood pressure (DBP) in subjects from the WCGS dataset.

The next plot, shows the use of log scales.

plot(
  wcgs,
  x=fit.([Normal], [wcgs.dbp]), y=:dbp,
  Stat.qq,
  Guide.xlabel("Theoretical quantiles"),
  Guide.ylabel("DBP (mm Hg)"),
  Scale.y_log10,
  Theme(default_color="IndianRed")
)
Theoretical quantiles 40 60 80 100 120 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5 51.0 51.5 52.0 52.5 53.0 53.5 54.0 54.5 55.0 55.5 56.0 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0 60.5 61.0 61.5 62.0 62.5 63.0 63.5 64.0 64.5 65.0 65.5 66.0 66.5 67.0 67.5 68.0 68.5 69.0 69.5 70.0 70.5 71.0 71.5 72.0 72.5 73.0 73.5 74.0 74.5 75.0 75.5 76.0 76.5 77.0 77.5 78.0 78.5 79.0 79.5 80.0 80.5 81.0 81.5 82.0 82.5 83.0 83.5 84.0 84.5 85.0 85.5 86.0 86.5 87.0 87.5 88.0 88.5 89.0 89.5 90.0 90.5 91.0 91.5 92.0 92.5 93.0 93.5 94.0 94.5 95.0 95.5 96.0 96.5 97.0 97.5 98.0 98.5 99.0 99.5 100.0 100.5 101.0 101.5 102.0 102.5 103.0 103.5 104.0 104.5 105.0 105.5 106.0 106.5 107.0 107.5 108.0 108.5 109.0 109.5 110.0 110.5 111.0 111.5 112.0 112.5 113.0 113.5 114.0 114.5 115.0 115.5 116.0 116.5 117.0 117.5 118.0 118.5 119.0 119.5 120.0 40 60 80 100 120 117.035981481795492.1548218294882684 114.153735707085422.12375044972156 112.733988583669592.112269189548135 111.767138574505132.103765042040625 111.02711579218942.0951708260906328 110.424518448946432.093421685162235 109.914518908144442.089905311518418 109.471338538285212.0863598306747484 109.078749295949582.0827898845784754 108.72585397840012.0791812460476247 108.404971121879732.0791812460476247 108.110477005942572.0755582408954956 107.838127274162322.0718820073061255 107.584637607771312.0718820073061255 107.347412949950812.0682041289774142 107.124366190847182.0644579892269186 106.91379297614282.0644579892269186 106.714282967168432.0644579892269186 106.524655491902252.0644579892269186 106.34391194486452.0607281185026407 106.171199952592372.0569048513364727 106.005785971926852.0569048513364727 105.847034041681212.0569048513364727 105.694389097163482.0569048513364727 105.547363717572882.0569048513364727 105.405527490320522.0531235847937506 105.268498394316372.0492180226701815 105.135935758067422.0492180226701815 105.00753445857712.0492180226701815 104.883020106993462.0492180226701815 104.762145025738122.0453810269624313 104.64468486556262.041392685158225 104.530435743844252.041392685158225 104.419211810389882.041392685158225 104.310843166139322.041392685158225 104.205174074949582.041392685158225 104.102061420164252.041392685158225 104.001373366726672.041392685158225 103.902988196755972.041392685158225 103.806793292208612.041392685158225 103.712684242821282.041392685158225 103.620564061216912.041392685158225 103.530342490046882.041392685158225 103.441935388480092.041392685158225 103.355264187349632.041392685158225 103.270255403913242.041392685158225 103.18684020854662.041392685158225 103.104954036820862.041392685158225 103.024536241361432.041392685158225 102.945529778677332.0375332875447594 102.867880926816242.03342375548695 102.791539030265072.03342375548695 102.716456268991012.03342375548695 102.642587448925212.03342375548695 102.569889811536612.03342375548695 102.498322860439972.03342375548695 102.42784820323652.03342375548695 102.3584294070042.03342375548695 102.290031866043052.03342375548695 102.22262268064882.03342375548695 102.156170545820342.03342375548695 102.090645648942672.03342375548695 102.026019575584672.029525675353313 101.96226522265022.0253058652647704 101.899356718201772.0253058652647704 101.837269347349582.0253058652647704 101.77597948366132.0253058652647704 101.715464525605342.0253058652647704 101.65570283758872.0253058652647704 101.596673695196122.0253058652647704 101.538357234274512.0253058652647704 101.480734403542612.0253058652647704 101.423786920435722.0253058652647704 101.367497229923422.0253058652647704 101.311848466062642.0253058652647704 101.256824416069852.0253058652647704 101.202409486716552.0233474291280094 101.148588672869442.0192134393118994 101.095347528012522.0170333392987803 101.042672136602682.0170333392987803 100.990549088123032.0170333392987803 100.93896545271052.0170333392987803 100.88790875824332.0170333392987803 100.837366968784862.0170333392987803 100.787328464288422.0170333392987803 100.737782021474572.0170333392987803 100.68871679580112.0170333392987803 100.640122304450662.0170333392987803 100.591988410268392.0170333392987803 100.544305306585582.0170333392987803 100.497063502871912.0170333392987803 100.45025381116172.0170333392987803 100.403867333205142.0170333392987803 100.357895448297732.0170333392987803 100.312329801745592.0170333392987803 100.267162293927232.0170333392987803 100.222385069914542.0170333392987803 100.177990509619352.0170333392987803 100.133971218433592.0170333392987803 100.090320018333782.0170333392987803 100.047029939422232.0170333392987803 100.004094211879232.0170333392987803 99.961506258302922.0170333392987803 99.919259686414072.0170333392987803 99.877348282105232.0130961677077743 99.835766002814922.0086001717619175 99.794506971208682.0086001717619175 99.753565469149782.0086001717619175 99.712935931944322.0086001717619175 99.672612942845152.0086001717619175 99.632591227801242.0086001717619175 99.592865650439142.0086001717619175 99.553431207264282.0086001717619175 99.51428302307092.0086001717619175 99.475416346549312.0086001717619175 99.436826546080822.0086001717619175 99.398509105710452.0086001717619175 99.360459621288642.0086001717619175 99.322673796773292.0086001717619175 99.28514744068442.0086001717619175 99.247876462703562.0086001717619175 99.210856870411562.004631386093095 99.174084766156852.0 99.137556344049262.0 99.101267887072452.0 99.065215764309842.0 99.029396428278352.0 98.993806412365362.0 98.958442328363842.0 98.923300864101072.0 98.888378781156962.0 98.853672912667922.0 98.819180161212072.0 98.784897496772612.0 98.75082195477582.0 98.716950634200062.0 98.683280695753382.0 98.649809360115942.0 98.616533906245152.0 98.583451669740642.0 98.550560041266252.0 98.517856465027242.0 98.485338437299832.0 98.453003505011282.0 98.420849264368262.0 98.388873359531772.0 98.357073481336292.0 98.325447366051892.0 98.293992794187282.0 98.26270758933222.0 98.231589617037682.0 98.20063678373272.0 98.169847035675732.0 98.139218357939912.0 98.108748773430522.0 98.078436341933452.0 98.048279159193852.0 98.018275356023112.0 97.988423097433942.0 97.958720581801882.0 97.92916604005272.0 97.899757734874272.0 97.870493959952542.0 97.841373039230322.0 97.812393326188312.0 97.783553203147492.0 97.754851080591982.0 97.726285396511952.0 97.697854615765582.0 97.669557229459562.0 97.641391754347482.0 97.613356732245382.0 97.585450729464042.0 97.557672336257332.0 97.530020166286012.0 97.502492856096722.0 97.47508906461531.9961040326592705 97.44780747265421.9912260756924949 97.420646782433581.9912260756924949 97.393605717115211.9912260756924949 97.366683020349441.9912260756924949 97.339877455834131.9912260756924949 97.313187806885611.9912260756924949 97.286612876021041.9912260756924949 97.2601514845521.9912260756924949 97.233802472188761.9912260756924949 97.207564696654981.9912260756924949 97.18143703331251.9912260756924949 97.1554183747961.9912260756924949 97.129507630656961.9912260756924949 97.103703727016961.9912260756924949 97.07800560622981.9912260756924949 97.052412226552241.9912260756924949 97.026922561823131.9912260756924949 97.001535601150551.9912260756924949 96.976250348607011.9912260756924949 96.951065822932011.9912260756924949 96.925981057242151.9912260756924949 96.900995098748471.9912260756924949 96.876107008480561.9912260756924949 96.851315861017571.9912260756924949 96.826620744225741.9912260756924949 96.802020759002261.9912260756924949 96.77751501902541.9912260756924949 96.75310265051051.9912260756924949 96.72878279197191.9912260756924949 96.704554593990551.9912260756924949 96.680417218986951.9912260756924949 96.656369840999641.9912260756924949 96.63241164546881.9912260756924949 96.608541829024821.9912260756924949 96.584759599281881.9912260756924949 96.56106417463631.9912260756924949 96.537454784069451.9912260756924949 96.513930666955191.9912260756924949 96.49049107287181.9912260756924949 96.467135261417971.9912260756924949 96.443862502033171.9912260756924949 96.42067207382191.9912260756924949 96.39756326538191.9912260756924949 96.374535374636271.9912260756924949 96.351587708669131.9912260756924949 96.328719583565121.9912260756924949 96.305930324252231.9912260756924949 96.283219264348251.9912260756924949 96.260585746010381.9912260756924949 96.238029119788211.987391733586353 96.215548744479861.9822712330395684 96.19314398699121.9822712330395684 96.170814222198031.9822712330395684 96.148558832811261.9822712330395684 96.126377209244951.9822712330395684 96.104268749487061.9822712330395684 96.0822328589731.9822712330395684 96.060268950461761.9822712330395684 96.03837644391471.9822712330395684 96.016554766376741.9822712330395684 95.99480335186011.9822712330395684 95.973121641230451.9822712330395684 95.95150908209521.9822712330395684 95.929965128694361.9822712330395684 95.90848924179341.9822712330395684 95.887080888578351.9822712330395684 95.865739542552971.9822712330395684 95.844464683438081.9822712330395684 95.823255797072831.9822712330395684 95.802112375317891.9822712330395684 95.781033915960681.9822712330395684 95.760019922622331.9822712330395684 95.739069904666681.9822712330395684 95.718183377110721.9822712330395684 95.697359860537161.9822712330395684 95.676598881008431.9822712330395684 95.655899969982441.9822712330395684 95.635262664229971.9822712330395684 95.614686505753641.9822712330395684 95.594171041708361.9822712330395684 95.573715824323471.9822712330395684 95.553320410826071.9822712330395684 95.532984363366151.9822712330395684 95.512707248942851.9822712330395684 95.492488639332151.9822712330395684 95.472328111016131.9822712330395684 95.45222524511321.9822712330395684 95.432179627309881.9822712330395684 95.412190847793821.9822712330395684 95.392258501187851.9822712330395684 95.372382186485521.9822712330395684 95.352561506987581.9822712330395684 95.332796070239781.9822712330395684 95.31308548797171.9822712330395684 95.293429376036711.9822712330395684 95.273827354353021.9822712330395684 95.254279046845781.9822712330395684 95.234784081390251.9822712330395684 95.21534208975591.9822712330395684 95.195952707551561.9822712330395684 95.176615574171541.9822712330395684 95.157330332742671.9822712330395684 95.13809663007231.9822712330395684 95.118914116597171.9822712330395684 95.099782446333221.9822712330395684 95.08070127682621.9822712330395684 95.061670269103221.9822712330395684 95.042689087625061.9822712330395684 95.023757400239381.9822712330395684 95.004874878134571.9822712330395684 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67.587209153008051.845098040014257 67.563936393623251.845098040014257 67.540580582169431.845098040014257 67.517140988086031.845098040014257 67.493616870971761.845098040014257 67.470007480404921.845098040014257 67.446312055759341.845098040014257 67.42252982601641.845098040014257 67.398660009572411.845098040014257 67.374701814041571.845098040014257 67.350654436054271.845098040014257 67.326517061050671.845098040014257 67.302288863069311.845098040014257 67.277969004530721.845098040014257 67.253556636015821.845098040014257 67.229050896038961.845098040014257 67.20445091081551.845098040014257 67.179755794023651.845098040014257 67.154964646560661.845098040014257 67.130076556292741.845098040014257 67.105090597799061.845098040014257 67.080005832109211.845098040014257 67.05482130643421.845098040014257 67.029536053890651.845098040014257 67.004149093218091.845098040014257 66.978659428488981.845098040014257 66.953066048811421.845098040014257 66.927367928024251.845098040014257 66.901564024384261.845098040014257 66.875653280245221.845098040014257 66.849634621728711.845098040014257 66.823506958386231.845098040014257 66.797269182852461.845098040014257 66.770920170489221.845098040014257 66.744458779020191.845098040014257 66.717883848155611.845098040014257 66.691194199207091.845098040014257 66.664388634691781.845098040014257 66.637465937926011.845098040014257 66.610424872607641.845098040014257 66.583264182387011.845098040014257 66.555982590425931.845098040014257 66.52857879894451.845098040014257 66.501051488755211.8381069631341054 66.473399318783891.8325089127062364 66.445620925577171.8325089127062364 66.417714922795841.8325089127062364 66.389679900693741.8325089127062364 66.361514425581661.8325089127062364 66.333217039275641.8325089127062364 66.304786258529261.8325089127062364 66.276220574449241.8325089127062364 66.247518451893731.8325089127062364 66.21867832885291.8325089127062364 66.18969861581091.8325089127062364 66.160577695088681.8325089127062364 66.131313920166951.8325089127062364 66.101905614988511.8325089127062364 66.072351073239331.8325089127062364 66.04264855760731.8325089127062364 66.01279629901811.8325089127062364 65.982792495847361.8325089127062364 65.952635313107751.8325089127062364 65.922322881610711.8325089127062364 65.89185329710131.8325089127062364 65.861224619365491.8325089127062364 65.830434871308511.8325089127062364 65.799482038003531.8325089127062364 65.768364065709021.8325089127062364 65.737078860853931.8325089127062364 65.705624288989331.8325089127062364 65.673998173704931.8325089127062364 65.642198295509441.8325089127062364 65.610222390672961.8325089127062364 65.578068150029941.8325089127062364 65.545733217741391.8325089127062364 65.513215190013981.8325089127062364 65.480511613774981.8325089127062364 65.447619985300581.8325089127062364 65.414537748796061.8325089127062364 65.381262294925281.8325089127062364 65.347790959287831.8325089127062364 65.314121020841161.8325089127062364 65.280249700265411.8325089127062364 65.24617415826861.8325089127062364 65.211891493829141.8325089127062364 65.17739874237331.8325089127062364 65.142692873884261.8325089127062364 65.107770790940171.8325089127062364 65.072629326677371.8325089127062364 65.037265242675861.8325089127062364 65.001675226762881.8325089127062364 64.965855890731381.8325089127062364 64.929803767968761.8325089127062364 64.893515310991941.8325089127062364 64.856986888884361.8325089127062364 64.820214784629661.8325089127062364 64.783195192337661.8325089127062364 64.745924214356831.8325089127062364 64.708397858267931.8325089127062364 64.670612033752581.8325089127062364 64.632562549330771.8325089127062364 64.594245108960411.8325089127062364 64.555655308491911.8325089127062364 64.516788631970311.8325089127062364 64.477640447776921.8325089127062364 64.438206004602081.825568087106352 64.398480427239971.8195439355418688 64.358458712196071.8195439355418688 64.31813572309691.8195439355418688 64.277506185891441.8195439355418688 64.236564683832541.8195439355418688 64.195305652226281.8195439355418688 64.1537233729361.8195439355418688 64.111811968627151.8195439355418688 64.06956539673831.8195439355418688 64.026977443161981.8195439355418688 63.9840417156189861.8195439355418688 63.940751636707441.8195439355418688 63.8971004366076161.8195439355418688 63.8530811454218751.8195439355418688 63.808686585126671.8195439355418688 63.763909361113991.8195439355418688 63.7187418532956261.8195439355418688 63.673176206743491.8195439355418688 63.627204321836071.8195439355418688 63.580817843879511.8195439355418688 63.5340081521693141.8195439355418688 63.486766348455631.8195439355418688 63.439083244772821.8195439355418688 63.390949350590561.8195439355418688 63.342354859240131.8195439355418688 63.293289633566641.8195439355418688 63.2437431907527951.8195439355418688 63.193704686256371.8195439355418688 63.143162896797921.8195439355418688 63.092106202330711.8195439355418688 63.0405225669181851.8195439355418688 62.9883995184385551.8195439355418688 62.9357241270286851.8195439355418688 62.882482982171781.8195439355418688 62.828662168324681.8195439355418688 62.774247238971381.8195439355418688 62.7192231889785751.8195439355418688 62.6635744251177941.8195439355418688 62.60728473460551.8195439355418688 62.55033725149861.8195439355418688 62.49271442076671.8195439355418688 62.43439795984511.8195439355418688 62.375368817452521.8195439355418688 62.315607129435861.8195439355418688 62.25509217137991.8195439355418688 62.193802307691651.8195439355418688 62.131714936839451.8195439355418688 62.0688064323910141.8195439355418688 62.005052079456531.8195439355418688 61.940426006098551.8195439355418688 61.874901109220871.8195439355418688 61.8084489743924051.8126098445178875 61.741039788998181.806179973983887 61.6726422480372351.806179973983887 61.603223451804721.806179973983887 61.532748794601241.806179973983887 61.4611818435046051.806179973983887 61.3884842061161.806179973983887 61.31461538605021.806179973983887 61.239532624776151.806179973983887 61.163190728224981.806179973983887 61.085541876363891.806179973983887 61.0065354136797641.806179973983887 60.926117618220361.806179973983887 60.844231446494621.806179973983887 60.760816251127981.806179973983887 60.67580746769161.806179973983887 60.5891362665611341.806179973983887 60.500729164994331.806179973983887 60.410507593824291.806179973983887 60.3183874122199551.806179973983887 60.224278362832611.806179973983887 60.128083458285241.806179973983887 60.0296982883145351.806179973983887 59.929010234876971.806179973983887 59.8258975800916351.806179973983887 59.720228488901881.806179973983887 59.6118598446513561.806179973983887 59.500635911196971.806179973983887 59.3863867894786141.806179973983887 59.268926629303081.806179973983887 59.148051548047761.806179973983887 59.023537196464121.806179973983887 58.895135896973781.7991656104907996 58.762573260724881.792391689498254 58.62554416472071.792391689498254 58.4837079374683241.792391689498254 58.336682557877721.792391689498254 58.1840376133600051.792391689498254 58.0252856831143551.792391689498254 57.859871702448841.7851789116017447 57.687159710176731.7781512503836436 57.506416163138981.7781512503836436 57.316788687872791.7781512503836436 57.117278678898391.7781512503836436 56.906705464194061.7781512503836436 56.683658705090411.7781512503836436 56.4464340472698751.7781512503836436 56.1929443808788561.7781512503836436 55.920594649098661.7781512503836436 55.626100533161491.7781512503836436 55.305217676641091.7781512503836436 54.9523223590916961.7781512503836436 54.559733116756021.7781512503836436 54.116552746896761.7781512503836436 53.60655320609471.7781512503836436 53.003955862851871.7781512503836436 52.263933080536091.7781512503836436 51.29708307137151.7707779516682645 49.877335947956061.7634279935629373 46.995090173245991.7634279935629373 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 101.7 101.8 101.9 102.0 102.1 102.2 101.68 101.70 101.72 101.74 101.76 101.78 101.80 101.82 101.84 101.86 101.88 101.90 101.92 101.94 101.96 101.98 102.00 102.02 102.04 102.06 102.08 102.10 102.12 102.14 102.16 102.18 102.20 101.700 101.702 101.704 101.706 101.708 101.710 101.712 101.714 101.716 101.718 101.720 101.722 101.724 101.726 101.728 101.730 101.732 101.734 101.736 101.738 101.740 101.742 101.744 101.746 101.748 101.750 101.752 101.754 101.756 101.758 101.760 101.762 101.764 101.766 101.768 101.770 101.772 101.774 101.776 101.778 101.780 101.782 101.784 101.786 101.788 101.790 101.792 101.794 101.796 101.798 101.800 101.802 101.804 101.806 101.808 101.810 101.812 101.814 101.816 101.818 101.820 101.822 101.824 101.826 101.828 101.830 101.832 101.834 101.836 101.838 101.840 101.842 101.844 101.846 101.848 101.850 101.852 101.854 101.856 101.858 101.860 101.862 101.864 101.866 101.868 101.870 101.872 101.874 101.876 101.878 101.880 101.882 101.884 101.886 101.888 101.890 101.892 101.894 101.896 101.898 101.900 101.902 101.904 101.906 101.908 101.910 101.912 101.914 101.916 101.918 101.920 101.922 101.924 101.926 101.928 101.930 101.932 101.934 101.936 101.938 101.940 101.942 101.944 101.946 101.948 101.950 101.952 101.954 101.956 101.958 101.960 101.962 101.964 101.966 101.968 101.970 101.972 101.974 101.976 101.978 101.980 101.982 101.984 101.986 101.988 101.990 101.992 101.994 101.996 101.998 102.000 102.002 102.004 102.006 102.008 102.010 102.012 102.014 102.016 102.018 102.020 102.022 102.024 102.026 102.028 102.030 102.032 102.034 102.036 102.038 102.040 102.042 102.044 102.046 102.048 102.050 102.052 102.054 102.056 102.058 102.060 102.062 102.064 102.066 102.068 102.070 102.072 102.074 102.076 102.078 102.080 102.082 102.084 102.086 102.088 102.090 102.092 102.094 102.096 102.098 102.100 102.102 102.104 102.106 102.108 102.110 102.112 102.114 102.116 102.118 102.120 102.122 102.124 102.126 102.128 102.130 102.132 102.134 102.136 102.138 102.140 102.142 102.144 102.146 102.148 102.150 102.152 102.154 102.156 102.158 102.160 102.162 102.164 102.166 102.168 102.170 102.172 102.174 102.176 102.178 102.180 102.182 102.184 102.186 102.188 102.190 102.192 102.194 102.196 102.198 102.200 102.202 101.6 101.8 102.0 102.2 DBP (mm Hg)
Figure 9: QQ-plot of diastolic blood pressure (DBP) in subjects from the WCGS dataset.

We can plot the log of the variable, instead of using log-scales.

qq_plot(log.(wcgs.dbp), ylab="log (DBP)")
Theoretical quantiles 3.5 4.0 4.5 5.0 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 3.500 3.505 3.510 3.515 3.520 3.525 3.530 3.535 3.540 3.545 3.550 3.555 3.560 3.565 3.570 3.575 3.580 3.585 3.590 3.595 3.600 3.605 3.610 3.615 3.620 3.625 3.630 3.635 3.640 3.645 3.650 3.655 3.660 3.665 3.670 3.675 3.680 3.685 3.690 3.695 3.700 3.705 3.710 3.715 3.720 3.725 3.730 3.735 3.740 3.745 3.750 3.755 3.760 3.765 3.770 3.775 3.780 3.785 3.790 3.795 3.800 3.805 3.810 3.815 3.820 3.825 3.830 3.835 3.840 3.845 3.850 3.855 3.860 3.865 3.870 3.875 3.880 3.885 3.890 3.895 3.900 3.905 3.910 3.915 3.920 3.925 3.930 3.935 3.940 3.945 3.950 3.955 3.960 3.965 3.970 3.975 3.980 3.985 3.990 3.995 4.000 4.005 4.010 4.015 4.020 4.025 4.030 4.035 4.040 4.045 4.050 4.055 4.060 4.065 4.070 4.075 4.080 4.085 4.090 4.095 4.100 4.105 4.110 4.115 4.120 4.125 4.130 4.135 4.140 4.145 4.150 4.155 4.160 4.165 4.170 4.175 4.180 4.185 4.190 4.195 4.200 4.205 4.210 4.215 4.220 4.225 4.230 4.235 4.240 4.245 4.250 4.255 4.260 4.265 4.270 4.275 4.280 4.285 4.290 4.295 4.300 4.305 4.310 4.315 4.320 4.325 4.330 4.335 4.340 4.345 4.350 4.355 4.360 4.365 4.370 4.375 4.380 4.385 4.390 4.395 4.400 4.405 4.410 4.415 4.420 4.425 4.430 4.435 4.440 4.445 4.450 4.455 4.460 4.465 4.470 4.475 4.480 4.485 4.490 4.495 4.500 4.505 4.510 4.515 4.520 4.525 4.530 4.535 4.540 4.545 4.550 4.555 4.560 4.565 4.570 4.575 4.580 4.585 4.590 4.595 4.600 4.605 4.610 4.615 4.620 4.625 4.630 4.635 4.640 4.645 4.650 4.655 4.660 4.665 4.670 4.675 4.680 4.685 4.690 4.695 4.700 4.705 4.710 4.715 4.720 4.725 4.730 4.735 4.740 4.745 4.750 4.755 4.760 4.765 4.770 4.775 4.780 4.785 4.790 4.795 4.800 4.805 4.810 4.815 4.820 4.825 4.830 4.835 4.840 4.845 4.850 4.855 4.860 4.865 4.870 4.875 4.880 4.885 4.890 4.895 4.900 4.905 4.910 4.915 4.920 4.925 4.930 4.935 4.940 4.945 4.950 4.955 4.960 4.965 4.970 4.975 4.980 4.985 4.990 4.995 5.000 3 4 5 4.8144272797157414.961660622637845 4.780334011353414.890116126768265 4.763540225025414.863679548244149 4.7521036302985484.844098024964735 4.7433501105490874.824309111432312 4.7362221573683154.820281565605037 4.73018951734788654.812184816071387 4.7249472623621724.804021044733257 4.7203034354850354.795800940069186 4.7161291367938584.787491742782046 4.7123335044309934.787491742782046 4.7088500170012014.779149465126912 4.7056284692152824.770684624465665 4.7026300117973974.770684624465665 4.6998239485559484.762215996652128 4.6971855916600194.7535901911063645 4.6946947807854474.7535901911063645 4.6923348334358444.7535901911063645 4.6900917837764954.7535901911063645 4.6879538195862154.745001846377848 4.6859108583808964.736198448394496 4.6839542232864184.736198448394496 4.682076391698154.736198448394496 4.6802707979131714.736198448394496 4.6785316763689794.736198448394496 4.6768539358370494.727491760420586 4.6752330574981824.718498871295094 4.6736650116458444.718498871295094 4.6721461890665884.718498871295094 4.6706733440924534.718498871295094 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4.1424177455008154.1588830833596715 4.1412798832391724.1588830833596715 4.14011611294861754.1588830833596715 4.1389251025022334.1588830833596715 4.1377054121337044.1588830833596715 4.1364554824035094.1588830833596715 4.1351736204252864.1588830833596715 4.1338579840403374.1588830833596715 4.1325065635608344.1588830833596715 4.1311171606175164.1588830833596715 4.12968736354062754.1588830833596715 4.1282145185664934.1588830833596715 4.12669569598723654.142731914543646 4.1251276501348994.127134385045092 4.1235067717960324.127134385045092 4.12182903126410154.127134385045092 4.1200899097199094.127134385045092 4.1182843159349314.127134385045092 4.1164064843466634.127134385045092 4.1144498492521854.110526350181512 4.1124068880468664.0943445622221 4.11026892385658554.0943445622221 4.1080258741972374.0943445622221 4.10566592684763254.0943445622221 4.10317511597306254.0943445622221 4.1005367590771334.0943445622221 4.0977306958356844.0943445622221 4.0947322384177984.0943445622221 4.091510690631884.0943445622221 4.08802720320208754.0943445622221 4.0842315708392234.0943445622221 4.0800572721480464.0943445622221 4.0754134452709084.0943445622221 4.0701711902851944.0943445622221 4.0641385502647644.0943445622221 4.0570105970839954.0943445622221 4.0482570773345324.0943445622221 4.036820482607674.077366914513876 4.0200266962796744.060443010546419 3.98593342791734354.060443010546419 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 4.0 4.5 5.0 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00 4.060 4.065 4.070 4.075 4.080 4.085 4.090 4.095 4.100 4.105 4.110 4.115 4.120 4.125 4.130 4.135 4.140 4.145 4.150 4.155 4.160 4.165 4.170 4.175 4.180 4.185 4.190 4.195 4.200 4.205 4.210 4.215 4.220 4.225 4.230 4.235 4.240 4.245 4.250 4.255 4.260 4.265 4.270 4.275 4.280 4.285 4.290 4.295 4.300 4.305 4.310 4.315 4.320 4.325 4.330 4.335 4.340 4.345 4.350 4.355 4.360 4.365 4.370 4.375 4.380 4.385 4.390 4.395 4.400 4.405 4.410 4.415 4.420 4.425 4.430 4.435 4.440 4.445 4.450 4.455 4.460 4.465 4.470 4.475 4.480 4.485 4.490 4.495 4.500 4.505 4.510 4.515 4.520 4.525 4.530 4.535 4.540 4.545 4.550 4.555 4.560 4.565 4.570 4.575 4.580 4.585 4.590 4.595 4.600 4.605 4.610 4.615 4.620 4.625 4.630 4.635 4.640 4.645 4.650 4.655 4.660 4.665 4.670 4.675 4.680 4.685 4.690 4.695 4.700 4.705 4.710 4.715 4.720 4.725 4.730 4.735 4.740 4.745 4.750 4.755 4.760 4.765 4.770 4.775 4.780 4.785 4.790 4.795 4.800 4.805 4.810 4.815 4.820 4.825 4.830 4.835 4.840 4.845 4.850 4.855 4.860 4.865 4.870 4.875 4.880 4.885 4.890 4.895 4.900 4.905 4.910 4.915 4.920 4.925 4.930 4.935 4.940 4.945 4.950 4.955 4.960 4.965 4 5 log (DBP)

4 Associations Between Continuous Variables

4.1 Scatter Plots

We use scatter plots to look at the relationship between two continuous variables. By default, the dependent variable (response) is plotted on the \(y\)-axis while the independent variable (explanatory) is plotted on the \(x\)-axis.

From the kfm dataset, let’s see if there is a relationship between the weight of the mother and the breast-milk intake of the child.

plot(
  kfm,
  x = :mat_weight, y = :dl_milk, color = :sex,
  Guide.xlabel("Maternal weight (kg)"),
  Guide.ylabel("Breast milk intake (dl/day) ")
)
Maternal weight (kg) 40 50 60 70 80 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 40.0 40.2 40.4 40.6 40.8 41.0 41.2 41.4 41.6 41.8 42.0 42.2 42.4 42.6 42.8 43.0 43.2 43.4 43.6 43.8 44.0 44.2 44.4 44.6 44.8 45.0 45.2 45.4 45.6 45.8 46.0 46.2 46.4 46.6 46.8 47.0 47.2 47.4 47.6 47.8 48.0 48.2 48.4 48.6 48.8 49.0 49.2 49.4 49.6 49.8 50.0 50.2 50.4 50.6 50.8 51.0 51.2 51.4 51.6 51.8 52.0 52.2 52.4 52.6 52.8 53.0 53.2 53.4 53.6 53.8 54.0 54.2 54.4 54.6 54.8 55.0 55.2 55.4 55.6 55.8 56.0 56.2 56.4 56.6 56.8 57.0 57.2 57.4 57.6 57.8 58.0 58.2 58.4 58.6 58.8 59.0 59.2 59.4 59.6 59.8 60.0 60.2 60.4 60.6 60.8 61.0 61.2 61.4 61.6 61.8 62.0 62.2 62.4 62.6 62.8 63.0 63.2 63.4 63.6 63.8 64.0 64.2 64.4 64.6 64.8 65.0 65.2 65.4 65.6 65.8 66.0 66.2 66.4 66.6 66.8 67.0 67.2 67.4 67.6 67.8 68.0 68.2 68.4 68.6 68.8 69.0 69.2 69.4 69.6 69.8 70.0 70.2 70.4 70.6 70.8 71.0 71.2 71.4 71.6 71.8 72.0 72.2 72.4 72.6 72.8 73.0 73.2 73.4 73.6 73.8 74.0 74.2 74.4 74.6 74.8 75.0 75.2 75.4 75.6 75.8 76.0 76.2 76.4 76.6 76.8 77.0 77.2 77.4 77.6 77.8 78.0 78.2 78.4 78.6 78.8 79.0 79.2 79.4 79.6 79.8 80.0 40 60 80 Boy Girl sex 47,5.82 67,6.97 48,4.63 62,9.03 48,7.24 51,6.46 59,7.36 55,8.23 49,6.91 50,7.68 55,5.03 74,7.93 58,7.74 65,5.17 70,8.57 58,4.44 61,8.06 63,7.01 58,7.22 53,6.89 59,6.9 80,8.67 73,5.0 67,7.42 58,10.03 63,7.7 49,4.91 78,10.35 54,6.84 52,5.62 76,10.43 59,8.39 60,5.97 68,9.63 59,6.78 62,9.32 56,8.39 68,7.71 54,8.73 58,7.64 58,6.48 57,8.05 57,8.43 78,9.79 56,6.29 58,6.44 55,9.65 62,8.41 48,8.44 65,8.42 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 4 6 8 10 12 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00 6.05 6.10 6.15 6.20 6.25 6.30 6.35 6.40 6.45 6.50 6.55 6.60 6.65 6.70 6.75 6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 7.30 7.35 7.40 7.45 7.50 7.55 7.60 7.65 7.70 7.75 7.80 7.85 7.90 7.95 8.00 8.05 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 9.05 9.10 9.15 9.20 9.25 9.30 9.35 9.40 9.45 9.50 9.55 9.60 9.65 9.70 9.75 9.80 9.85 9.90 9.95 10.00 10.05 10.10 10.15 10.20 10.25 10.30 10.35 10.40 10.45 10.50 10.55 10.60 10.65 10.70 10.75 10.80 10.85 10.90 10.95 11.00 11.05 11.10 11.15 11.20 11.25 11.30 11.35 11.40 11.45 11.50 11.55 11.60 11.65 11.70 11.75 11.80 11.85 11.90 11.95 12.00 4 6 8 10 12 Breast milk intake (dl/day)
Figure 10: Relationship between maternal weight and breast-milk intake in infants.
Note

We can extend plots by adding new layers. In the following example, we use two layers: one for the scatter plot and a second to add a line representing a linear fit.

plot(
  kfm,
  x = :mat_weight, y = :dl_milk, color = :sex,
  Geom.point, 
  layer(
    Stat.smooth(method=:lm), 
    Geom.line, 
    Geom.ribbon
    ),
    Guide.xlabel("Maternal weight (kg)"),
    Guide.ylabel("Breast milk intake (dl/day) ")
)
Maternal weight (kg) 40 50 60 70 80 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 40.0 40.2 40.4 40.6 40.8 41.0 41.2 41.4 41.6 41.8 42.0 42.2 42.4 42.6 42.8 43.0 43.2 43.4 43.6 43.8 44.0 44.2 44.4 44.6 44.8 45.0 45.2 45.4 45.6 45.8 46.0 46.2 46.4 46.6 46.8 47.0 47.2 47.4 47.6 47.8 48.0 48.2 48.4 48.6 48.8 49.0 49.2 49.4 49.6 49.8 50.0 50.2 50.4 50.6 50.8 51.0 51.2 51.4 51.6 51.8 52.0 52.2 52.4 52.6 52.8 53.0 53.2 53.4 53.6 53.8 54.0 54.2 54.4 54.6 54.8 55.0 55.2 55.4 55.6 55.8 56.0 56.2 56.4 56.6 56.8 57.0 57.2 57.4 57.6 57.8 58.0 58.2 58.4 58.6 58.8 59.0 59.2 59.4 59.6 59.8 60.0 60.2 60.4 60.6 60.8 61.0 61.2 61.4 61.6 61.8 62.0 62.2 62.4 62.6 62.8 63.0 63.2 63.4 63.6 63.8 64.0 64.2 64.4 64.6 64.8 65.0 65.2 65.4 65.6 65.8 66.0 66.2 66.4 66.6 66.8 67.0 67.2 67.4 67.6 67.8 68.0 68.2 68.4 68.6 68.8 69.0 69.2 69.4 69.6 69.8 70.0 70.2 70.4 70.6 70.8 71.0 71.2 71.4 71.6 71.8 72.0 72.2 72.4 72.6 72.8 73.0 73.2 73.4 73.6 73.8 74.0 74.2 74.4 74.6 74.8 75.0 75.2 75.4 75.6 75.8 76.0 76.2 76.4 76.6 76.8 77.0 77.2 77.4 77.6 77.8 78.0 78.2 78.4 78.6 78.8 79.0 79.2 79.4 79.6 79.8 80.0 40 60 80 Boy Girl sex 47,5.82 67,6.97 48,4.63 62,9.03 48,7.24 51,6.46 59,7.36 55,8.23 49,6.91 50,7.68 55,5.03 74,7.93 58,7.74 65,5.17 70,8.57 58,4.44 61,8.06 63,7.01 58,7.22 53,6.89 59,6.9 80,8.67 73,5.0 67,7.42 58,10.03 63,7.7 49,4.91 78,10.35 54,6.84 52,5.62 76,10.43 59,8.39 60,5.97 68,9.63 59,6.78 62,9.32 56,8.39 68,7.71 54,8.73 58,7.64 58,6.48 57,8.05 57,8.43 78,9.79 56,6.29 58,6.44 55,9.65 62,8.41 48,8.44 65,8.42 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 4 6 8 10 12 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00 6.05 6.10 6.15 6.20 6.25 6.30 6.35 6.40 6.45 6.50 6.55 6.60 6.65 6.70 6.75 6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 7.30 7.35 7.40 7.45 7.50 7.55 7.60 7.65 7.70 7.75 7.80 7.85 7.90 7.95 8.00 8.05 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 9.05 9.10 9.15 9.20 9.25 9.30 9.35 9.40 9.45 9.50 9.55 9.60 9.65 9.70 9.75 9.80 9.85 9.90 9.95 10.00 10.05 10.10 10.15 10.20 10.25 10.30 10.35 10.40 10.45 10.50 10.55 10.60 10.65 10.70 10.75 10.80 10.85 10.90 10.95 11.00 11.05 11.10 11.15 11.20 11.25 11.30 11.35 11.40 11.45 11.50 11.55 11.60 11.65 11.70 11.75 11.80 11.85 11.90 11.95 12.00 4 6 8 10 12 Breast milk intake (dl/day)
Figure 11: Relationship between maternal weight and breast-milk intake in infants.

In the next plot, instead of showing the linear fit, we add a loess trend with a smoother:

plot(
  kfm,
  x = :mat_weight, y = :dl_milk, xgroup = :sex,
  Geom.subplot_grid(Geom.point, Geom.smooth(smoothing=0.9)),
  Guide.xlabel("Maternal weight (kg)"),
  Guide.ylabel("Breast milk intake (dl/day) ")
)
Maternal weight (kg) Girl Boy 40 50 60 70 80 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 40.0 40.2 40.4 40.6 40.8 41.0 41.2 41.4 41.6 41.8 42.0 42.2 42.4 42.6 42.8 43.0 43.2 43.4 43.6 43.8 44.0 44.2 44.4 44.6 44.8 45.0 45.2 45.4 45.6 45.8 46.0 46.2 46.4 46.6 46.8 47.0 47.2 47.4 47.6 47.8 48.0 48.2 48.4 48.6 48.8 49.0 49.2 49.4 49.6 49.8 50.0 50.2 50.4 50.6 50.8 51.0 51.2 51.4 51.6 51.8 52.0 52.2 52.4 52.6 52.8 53.0 53.2 53.4 53.6 53.8 54.0 54.2 54.4 54.6 54.8 55.0 55.2 55.4 55.6 55.8 56.0 56.2 56.4 56.6 56.8 57.0 57.2 57.4 57.6 57.8 58.0 58.2 58.4 58.6 58.8 59.0 59.2 59.4 59.6 59.8 60.0 60.2 60.4 60.6 60.8 61.0 61.2 61.4 61.6 61.8 62.0 62.2 62.4 62.6 62.8 63.0 63.2 63.4 63.6 63.8 64.0 64.2 64.4 64.6 64.8 65.0 65.2 65.4 65.6 65.8 66.0 66.2 66.4 66.6 66.8 67.0 67.2 67.4 67.6 67.8 68.0 68.2 68.4 68.6 68.8 69.0 69.2 69.4 69.6 69.8 70.0 70.2 70.4 70.6 70.8 71.0 71.2 71.4 71.6 71.8 72.0 72.2 72.4 72.6 72.8 73.0 73.2 73.4 73.6 73.8 74.0 74.2 74.4 74.6 74.8 75.0 75.2 75.4 75.6 75.8 76.0 76.2 76.4 76.6 76.8 77.0 77.2 77.4 77.6 77.8 78.0 78.2 78.4 78.6 78.8 79.0 79.2 79.4 79.6 79.8 80.0 40 60 80 40 50 60 70 80 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 40.0 40.2 40.4 40.6 40.8 41.0 41.2 41.4 41.6 41.8 42.0 42.2 42.4 42.6 42.8 43.0 43.2 43.4 43.6 43.8 44.0 44.2 44.4 44.6 44.8 45.0 45.2 45.4 45.6 45.8 46.0 46.2 46.4 46.6 46.8 47.0 47.2 47.4 47.6 47.8 48.0 48.2 48.4 48.6 48.8 49.0 49.2 49.4 49.6 49.8 50.0 50.2 50.4 50.6 50.8 51.0 51.2 51.4 51.6 51.8 52.0 52.2 52.4 52.6 52.8 53.0 53.2 53.4 53.6 53.8 54.0 54.2 54.4 54.6 54.8 55.0 55.2 55.4 55.6 55.8 56.0 56.2 56.4 56.6 56.8 57.0 57.2 57.4 57.6 57.8 58.0 58.2 58.4 58.6 58.8 59.0 59.2 59.4 59.6 59.8 60.0 60.2 60.4 60.6 60.8 61.0 61.2 61.4 61.6 61.8 62.0 62.2 62.4 62.6 62.8 63.0 63.2 63.4 63.6 63.8 64.0 64.2 64.4 64.6 64.8 65.0 65.2 65.4 65.6 65.8 66.0 66.2 66.4 66.6 66.8 67.0 67.2 67.4 67.6 67.8 68.0 68.2 68.4 68.6 68.8 69.0 69.2 69.4 69.6 69.8 70.0 70.2 70.4 70.6 70.8 71.0 71.2 71.4 71.6 71.8 72.0 72.2 72.4 72.6 72.8 73.0 73.2 73.4 73.6 73.8 74.0 74.2 74.4 74.6 74.8 75.0 75.2 75.4 75.6 75.8 76.0 76.2 76.4 76.6 76.8 77.0 77.2 77.4 77.6 77.8 78.0 78.2 78.4 78.6 78.8 79.0 79.2 79.4 79.6 79.8 80.0 40 60 80 47,5.82 67,6.97 48,4.63 62,9.03 48,7.24 51,6.46 59,7.36 55,8.23 49,6.91 50,7.68 55,5.03 74,7.93 58,7.74 65,5.17 70,8.57 58,4.44 61,8.06 63,7.01 58,7.22 53,6.89 59,6.9 80,8.67 73,5.0 67,7.42 58,10.03 63,7.7 49,4.91 78,10.35 54,6.84 52,5.62 76,10.43 59,8.39 60,5.97 68,9.63 59,6.78 62,9.32 56,8.39 68,7.71 54,8.73 58,7.64 58,6.48 57,8.05 57,8.43 78,9.79 56,6.29 58,6.44 55,9.65 62,8.41 48,8.44 65,8.42 4 6 8 10 12 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00 6.05 6.10 6.15 6.20 6.25 6.30 6.35 6.40 6.45 6.50 6.55 6.60 6.65 6.70 6.75 6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 7.30 7.35 7.40 7.45 7.50 7.55 7.60 7.65 7.70 7.75 7.80 7.85 7.90 7.95 8.00 8.05 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 9.05 9.10 9.15 9.20 9.25 9.30 9.35 9.40 9.45 9.50 9.55 9.60 9.65 9.70 9.75 9.80 9.85 9.90 9.95 10.00 10.05 10.10 10.15 10.20 10.25 10.30 10.35 10.40 10.45 10.50 10.55 10.60 10.65 10.70 10.75 10.80 10.85 10.90 10.95 11.00 11.05 11.10 11.15 11.20 11.25 11.30 11.35 11.40 11.45 11.50 11.55 11.60 11.65 11.70 11.75 11.80 11.85 11.90 11.95 12.00 4 6 8 10 12 Breast milk intake (dl/day)
Figure 12: Relationship between maternal weight and breast-milk intake in infants.

In the next plot, we use different line colours and different symbols (by sex):

plot(
  kfm,
  x = :mat_weight, y = :dl_milk, 
  color = :sex, shape = :sex,
  Geom.point, Geom.smooth(method = :lm),
  Guide.xlabel("Maternal weight (kg)"),
  Guide.ylabel("Breast milk intake (dl/day) ")
)
Maternal weight (kg) 40 50 60 70 80 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 40.0 40.2 40.4 40.6 40.8 41.0 41.2 41.4 41.6 41.8 42.0 42.2 42.4 42.6 42.8 43.0 43.2 43.4 43.6 43.8 44.0 44.2 44.4 44.6 44.8 45.0 45.2 45.4 45.6 45.8 46.0 46.2 46.4 46.6 46.8 47.0 47.2 47.4 47.6 47.8 48.0 48.2 48.4 48.6 48.8 49.0 49.2 49.4 49.6 49.8 50.0 50.2 50.4 50.6 50.8 51.0 51.2 51.4 51.6 51.8 52.0 52.2 52.4 52.6 52.8 53.0 53.2 53.4 53.6 53.8 54.0 54.2 54.4 54.6 54.8 55.0 55.2 55.4 55.6 55.8 56.0 56.2 56.4 56.6 56.8 57.0 57.2 57.4 57.6 57.8 58.0 58.2 58.4 58.6 58.8 59.0 59.2 59.4 59.6 59.8 60.0 60.2 60.4 60.6 60.8 61.0 61.2 61.4 61.6 61.8 62.0 62.2 62.4 62.6 62.8 63.0 63.2 63.4 63.6 63.8 64.0 64.2 64.4 64.6 64.8 65.0 65.2 65.4 65.6 65.8 66.0 66.2 66.4 66.6 66.8 67.0 67.2 67.4 67.6 67.8 68.0 68.2 68.4 68.6 68.8 69.0 69.2 69.4 69.6 69.8 70.0 70.2 70.4 70.6 70.8 71.0 71.2 71.4 71.6 71.8 72.0 72.2 72.4 72.6 72.8 73.0 73.2 73.4 73.6 73.8 74.0 74.2 74.4 74.6 74.8 75.0 75.2 75.4 75.6 75.8 76.0 76.2 76.4 76.6 76.8 77.0 77.2 77.4 77.6 77.8 78.0 78.2 78.4 78.6 78.8 79.0 79.2 79.4 79.6 79.8 80.0 40 60 80 Boy Girl sex 47,5.82 67,6.97 48,4.63 62,9.03 48,7.24 51,6.46 59,7.36 55,8.23 49,6.91 50,7.68 55,5.03 74,7.93 58,7.74 65,5.17 70,8.57 58,4.44 61,8.06 63,7.01 58,7.22 53,6.89 59,6.9 80,8.67 73,5.0 67,7.42 58,10.03 63,7.7 49,4.91 78,10.35 54,6.84 52,5.62 76,10.43 59,8.39 60,5.97 68,9.63 59,6.78 62,9.32 56,8.39 68,7.71 54,8.73 58,7.64 58,6.48 57,8.05 57,8.43 78,9.79 56,6.29 58,6.44 55,9.65 62,8.41 48,8.44 65,8.42 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 4 6 8 10 12 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00 6.05 6.10 6.15 6.20 6.25 6.30 6.35 6.40 6.45 6.50 6.55 6.60 6.65 6.70 6.75 6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 7.30 7.35 7.40 7.45 7.50 7.55 7.60 7.65 7.70 7.75 7.80 7.85 7.90 7.95 8.00 8.05 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 9.05 9.10 9.15 9.20 9.25 9.30 9.35 9.40 9.45 9.50 9.55 9.60 9.65 9.70 9.75 9.80 9.85 9.90 9.95 10.00 10.05 10.10 10.15 10.20 10.25 10.30 10.35 10.40 10.45 10.50 10.55 10.60 10.65 10.70 10.75 10.80 10.85 10.90 10.95 11.00 11.05 11.10 11.15 11.20 11.25 11.30 11.35 11.40 11.45 11.50 11.55 11.60 11.65 11.70 11.75 11.80 11.85 11.90 11.95 12.00 4 6 8 10 12 Breast milk intake (dl/day)
Figure 13: Relationship between maternal weight and breast-milk intake in infants.

4.2 Line Charts

In this example, our dataset is in wide format.

Reshaping wide to long data:

flu_melt = stack(flu, Not(:week))
flu_melt |> head
5×3 DataFrame
Row week variable value
Date String Int64
1 1957-08-25 child 0
2 1957-09-01 child 0
3 1957-09-08 child 0
4 1957-09-15 child 23
5 1957-09-22 child 63
plot(
  flu_melt,
  x = :week, y = :value, color = :variable,
  Geom.point, Geom.path,
  Guide.xlabel("Date"),
  Guide.ylabel("Number of cases"),
  Guide.colorkey("Age group")
)
Date Aug 1, 1957 Sep Oct Nov Dec Jan 1958 Jul 30, 1957 Aug 6 13 20 27 Sep 3 10 17 24 Oct 1 8 15 22 29 Nov 5 12 19 26 Dec 3 10 17 24 31 Jan 7, 1958 Aug 1, 1957 Sep Oct Nov Dec Jan 1958 Jul 1, 1957 Oct Jan 1958 child young mid old Age group 1957-12-292 1957-12-221 1957-12-150 1957-12-086 1957-12-010 1957-11-242 1957-11-175 1957-11-103 1957-11-035 1957-10-276 1957-10-2012 1957-10-1329 1957-10-067 1957-09-2927 1957-09-2241 1957-09-1511 1957-09-082 1957-09-011 1957-08-251 1957-12-296 1957-12-227 1957-12-153 1957-12-084 1957-12-013 1957-11-242 1957-11-176 1957-11-1011 1957-11-0316 1957-10-2713 1957-10-2033 1957-10-1387 1957-10-06143 1957-09-29171 1957-09-22173 1957-09-1563 1957-09-084 1957-09-016 1957-08-251 1957-12-291 1957-12-221 1957-12-151 1957-12-081 1957-12-011 1957-11-242 1957-11-171 1957-11-106 1957-11-036 1957-10-274 1957-10-2018 1957-10-1340 1957-10-06150 1957-09-29207 1957-09-22208 1957-09-1573 1957-09-082 1957-09-012 1957-08-250 1957-12-291 1957-12-222 1957-12-150 1957-12-080 1957-12-010 1957-11-240 1957-11-170 1957-11-101 1957-11-032 1957-10-273 1957-10-2017 1957-10-1326 1957-10-0666 1957-09-2973 1957-09-2263 1957-09-1523 1957-09-080 1957-09-010 1957-08-250 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 0 250 Number of cases
Figure 14: Dynamics of reported influenza cases by age group, in the 1957 pandemic in England and Wales.

5 Comparing Groups

5.1 Box-Plots

When we are comparing continuous variables, between two or more groups, box plots are the best option, particularly if the number of observations in the groups is relatively large \((\geq 30)\).

plot(
  @subset(wcgs, !ismissing(:chol)),
  x = :chd, y = :chol,
  Geom.boxplot,
  Guide.xlabel("Coronary Heart Disease"),
  Guide.ylabel("Cholesterol (mg/dl)")
)
Coronary Heart Disease No CHD CHD h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0 200 400 600 800 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 0 1000 Cholesterol (mg/dl)
Figure 15: Box plots of blood cholesterol by coronary heart disease (CHD) event from the WCGS dataset.

In the previous figure the presence of an outlier is clear. If we would like to remove that outlier, we would need to declare that in the report. For demonstration purposes, if we do not want to show the outlier in the plot, we have the option to filter the data using the @subset command.

plot(
  @subset(wcgs |> dropmissing, :chol .< 500),
  x = :chd, y = :chol,
  Geom.boxplot,
  Guide.xlabel("Coronary Heart Disease"),
  Guide.ylabel("Cholesterol (mg/dl)"),
  Theme(default_color="MidnightBlue")
)
Coronary Heart Disease No CHD CHD h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0 100 200 300 400 500 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 160 162 164 166 168 170 172 174 176 178 180 182 184 186 188 190 192 194 196 198 200 202 204 206 208 210 212 214 216 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246 248 250 252 254 256 258 260 262 264 266 268 270 272 274 276 278 280 282 284 286 288 290 292 294 296 298 300 302 304 306 308 310 312 314 316 318 320 322 324 326 328 330 332 334 336 338 340 342 344 346 348 350 352 354 356 358 360 362 364 366 368 370 372 374 376 378 380 382 384 386 388 390 392 394 396 398 400 402 404 406 408 410 412 414 416 418 420 422 424 426 428 430 432 434 436 438 440 442 444 446 448 450 452 454 456 458 460 462 464 466 468 470 472 474 476 478 480 482 484 486 488 490 492 494 496 498 500 0 500 Cholesterol (mg/dl)
plot(
  birth,
  x = :race, y = :bwt, color = :smoke,
  Geom.boxplot,
  Guide.xlabel(""),
  Guide.ylabel("Birth weight (g)"),
  Guide.colorkey("")
)
African-American Other White Non-smoker Smoker h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0 1000 2000 3000 4000 5000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800 820 840 860 880 900 920 940 960 980 1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200 1220 1240 1260 1280 1300 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 2120 2140 2160 2180 2200 2220 2240 2260 2280 2300 2320 2340 2360 2380 2400 2420 2440 2460 2480 2500 2520 2540 2560 2580 2600 2620 2640 2660 2680 2700 2720 2740 2760 2780 2800 2820 2840 2860 2880 2900 2920 2940 2960 2980 3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200 3220 3240 3260 3280 3300 3320 3340 3360 3380 3400 3420 3440 3460 3480 3500 3520 3540 3560 3580 3600 3620 3640 3660 3680 3700 3720 3740 3760 3780 3800 3820 3840 3860 3880 3900 3920 3940 3960 3980 4000 4020 4040 4060 4080 4100 4120 4140 4160 4180 4200 4220 4240 4260 4280 4300 4320 4340 4360 4380 4400 4420 4440 4460 4480 4500 4520 4540 4560 4580 4600 4620 4640 4660 4680 4700 4720 4740 4760 4780 4800 4820 4840 4860 4880 4900 4920 4940 4960 4980 5000 0 5000 Birth weight (g)
Figure 16: Comparison of birth weight distributions by ethnicity and smoking status of the mother.

Faceting:

plot(
  birth,
  x = :Race, y = :bwt, color=:Race, xgroup = :smoke,
  Geom.subplot_grid(Geom.boxplot),
  Guide.xlabel(""),
  Guide.ylabel("Birth weight (g)"),
  Guide.colorkey("")
)
Non-white White Smoker Non-smoker Non-white White Non-white White 0 1000 2000 3000 4000 5000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800 820 840 860 880 900 920 940 960 980 1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200 1220 1240 1260 1280 1300 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 2120 2140 2160 2180 2200 2220 2240 2260 2280 2300 2320 2340 2360 2380 2400 2420 2440 2460 2480 2500 2520 2540 2560 2580 2600 2620 2640 2660 2680 2700 2720 2740 2760 2780 2800 2820 2840 2860 2880 2900 2920 2940 2960 2980 3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200 3220 3240 3260 3280 3300 3320 3340 3360 3380 3400 3420 3440 3460 3480 3500 3520 3540 3560 3580 3600 3620 3640 3660 3680 3700 3720 3740 3760 3780 3800 3820 3840 3860 3880 3900 3920 3940 3960 3980 4000 4020 4040 4060 4080 4100 4120 4140 4160 4180 4200 4220 4240 4260 4280 4300 4320 4340 4360 4380 4400 4420 4440 4460 4480 4500 4520 4540 4560 4580 4600 4620 4640 4660 4680 4700 4720 4740 4760 4780 4800 4820 4840 4860 4880 4900 4920 4940 4960 4980 5000 0 5000 Birth weight (g)
Figure 17: Comparison of birth weight distributions by ethnicity and smoking status of the mother.

5.2 Strip Charts

When we want to compare groups and the number of observations is relatively small \((n<30)\), strip charts are superior than box-plots as we can show all observations.

strip_error(
  energy, "stature", "expend",
  xlab = "Stature",
  ylab = "Energy expenditure (MJ)"
)
Stature obese lean 110.297777777777778 28.066153846153847 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 6 8 10 12 14 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00 6.05 6.10 6.15 6.20 6.25 6.30 6.35 6.40 6.45 6.50 6.55 6.60 6.65 6.70 6.75 6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 7.30 7.35 7.40 7.45 7.50 7.55 7.60 7.65 7.70 7.75 7.80 7.85 7.90 7.95 8.00 8.05 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 9.05 9.10 9.15 9.20 9.25 9.30 9.35 9.40 9.45 9.50 9.55 9.60 9.65 9.70 9.75 9.80 9.85 9.90 9.95 10.00 10.05 10.10 10.15 10.20 10.25 10.30 10.35 10.40 10.45 10.50 10.55 10.60 10.65 10.70 10.75 10.80 10.85 10.90 10.95 11.00 11.05 11.10 11.15 11.20 11.25 11.30 11.35 11.40 11.45 11.50 11.55 11.60 11.65 11.70 11.75 11.80 11.85 11.90 11.95 12.00 12.05 12.10 12.15 12.20 12.25 12.30 12.35 12.40 12.45 12.50 12.55 12.60 12.65 12.70 12.75 12.80 12.85 12.90 12.95 13.00 13.05 13.10 13.15 13.20 13.25 13.30 13.35 13.40 13.45 13.50 13.55 13.60 13.65 13.70 13.75 13.80 13.85 13.90 13.95 14.00 5 10 15 Energy expenditure (MJ)
Figure 18: Comparison of energy expenditure between obese and lean women.

5.3 Error Bars

birth_bst = combine(groupby(birth, [:smoke, :race]), :bwt => cis => AsTable)
6×5 DataFrame
Row smoke race outcome lower upper
Cat… Cat… Float64 Float64 Float64
1 Non-smoker White 3428.75 3218.93 3638.57
2 Non-smoker African-American 2854.5 2550.09 3158.91
3 Non-smoker Other 2815.78 2628.31 3003.25
4 Smoker White 2826.85 2656.57 2997.12
5 Smoker African-American 2504.0 2109.15 2898.85
6 Smoker Other 2757.17 2298.84 3215.49
plot(
  birth_bst,
  x=:race, y=:outcome, xgroup=:smoke,
  ymin=:lower, ymax=:upper,
  Geom.subplot_grid(
    Geom.point,
    Geom.errorbar
    ),
  Guide.ylabel("Birth weight (g)"),
  Guide.xlabel(""),
  Theme(default_color="Firebrick")
)
Smoker Non-smoker White African-American Other White African-American Other 32757.1666666666665 2,2504.0 12826.846153846154 32815.7818181818184 2,2854.5 1,3428.75 2000 2500 3000 3500 4000 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 2110 2120 2130 2140 2150 2160 2170 2180 2190 2200 2210 2220 2230 2240 2250 2260 2270 2280 2290 2300 2310 2320 2330 2340 2350 2360 2370 2380 2390 2400 2410 2420 2430 2440 2450 2460 2470 2480 2490 2500 2510 2520 2530 2540 2550 2560 2570 2580 2590 2600 2610 2620 2630 2640 2650 2660 2670 2680 2690 2700 2710 2720 2730 2740 2750 2760 2770 2780 2790 2800 2810 2820 2830 2840 2850 2860 2870 2880 2890 2900 2910 2920 2930 2940 2950 2960 2970 2980 2990 3000 3010 3020 3030 3040 3050 3060 3070 3080 3090 3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200 3210 3220 3230 3240 3250 3260 3270 3280 3290 3300 3310 3320 3330 3340 3350 3360 3370 3380 3390 3400 3410 3420 3430 3440 3450 3460 3470 3480 3490 3500 3510 3520 3530 3540 3550 3560 3570 3580 3590 3600 3610 3620 3630 3640 3650 3660 3670 3680 3690 3700 3710 3720 3730 3740 3750 3760 3770 3780 3790 3800 3810 3820 3830 3840 3850 3860 3870 3880 3890 3900 3910 3920 3930 3940 3950 3960 3970 3980 3990 4000 2000 4000 Birth weight (g)
Figure 19: Comparison of birth-weight by ethnicity and smoking status of the mother.

5.4 Violin Plots

Violin plots are an alternative to box-plots.

plot(
  kfm,
  x = :sex, y = :dl_milk,
  Geom.violin,
  Guide.xlabel(""),
  Guide.ylabel("Breast milk intake (dl/day) "),
  Theme(default_color="Plum")
)
Boy Girl h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0 5 10 15 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00 6.05 6.10 6.15 6.20 6.25 6.30 6.35 6.40 6.45 6.50 6.55 6.60 6.65 6.70 6.75 6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 7.30 7.35 7.40 7.45 7.50 7.55 7.60 7.65 7.70 7.75 7.80 7.85 7.90 7.95 8.00 8.05 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 9.05 9.10 9.15 9.20 9.25 9.30 9.35 9.40 9.45 9.50 9.55 9.60 9.65 9.70 9.75 9.80 9.85 9.90 9.95 10.00 10.05 10.10 10.15 10.20 10.25 10.30 10.35 10.40 10.45 10.50 10.55 10.60 10.65 10.70 10.75 10.80 10.85 10.90 10.95 11.00 11.05 11.10 11.15 11.20 11.25 11.30 11.35 11.40 11.45 11.50 11.55 11.60 11.65 11.70 11.75 11.80 11.85 11.90 11.95 12.00 12.05 12.10 12.15 12.20 12.25 12.30 12.35 12.40 12.45 12.50 12.55 12.60 12.65 12.70 12.75 12.80 12.85 12.90 12.95 13.00 13.05 13.10 13.15 13.20 13.25 13.30 13.35 13.40 13.45 13.50 13.55 13.60 13.65 13.70 13.75 13.80 13.85 13.90 13.95 14.00 14.05 14.10 14.15 14.20 14.25 14.30 14.35 14.40 14.45 14.50 14.55 14.60 14.65 14.70 14.75 14.80 14.85 14.90 14.95 15.00 0 20 Breast milk intake (dl/day)
Figure 20: Comparison of breast-milk intake by sex.
plot(
  wcgs,
  x = :beh_pat, y = :sbp, color = :beh_pat, xgroup=:chd,
  Geom.subplot_grid(Geom.violin),
  Guide.xlabel("Coronary Heart Disease status"),
  Guide.ylabel("SBP (mmHg)"),
  Guide.colorkey("Behaviour \n Pattern")
)
Coronary Heart Disease status A2 B3 B4 A1 Behaviour Pattern CHD No CHD A2 B3 B4 A1 A2 B3 B4 A1 0 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 0 250 SBP (mmHg)
Figure 21: Comparison of systolic blood pressure (SBP) by coronary heart disease event and behaviour pattern group.

5.5 Bar Charts

Bar charts or bar plots are used, most of the time, to display information from a table graphically. Therefore, for publications are not the best option as a table uses less space and contains better information.

5.5.1 Frequency

For categorical variables, we can plot the counts with frequency.

@combine(groupby(birth, [:race, :low]), :count = @nrow)
6×3 DataFrame
Row race low count
Cat… Cat… Int64
1 White No 73
2 White Yes 23
3 African-American No 15
4 African-American Yes 11
5 Other No 42
6 Other Yes 25
plot(
  @combine(groupby(birth, [:race, :low]), :count = @nrow),
  x = :race, y = :count, color = :low,
  Geom.bar(position=:dodge),
  Guide.xlabel(""),
  Guide.colorkey(title="Low birth weight?", pos=[0.4w, -0.3h])
)
White African-American Other h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? No Yes Low birth weight? 0 20 40 60 80 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5 51.0 51.5 52.0 52.5 53.0 53.5 54.0 54.5 55.0 55.5 56.0 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0 60.5 61.0 61.5 62.0 62.5 63.0 63.5 64.0 64.5 65.0 65.5 66.0 66.5 67.0 67.5 68.0 68.5 69.0 69.5 70.0 70.5 71.0 71.5 72.0 72.5 73.0 73.5 74.0 74.5 75.0 75.5 76.0 76.5 77.0 77.5 78.0 78.5 79.0 79.5 80.0 0 100 count
Figure 22: Comparison of low-birth babies by ethnicity.

5.5.2 Expectation

For continuous variables, we can plot the expected (mean) values, with expectation.

combine(groupby(kfm, :sex), :dl_milk => cis => AsTable)
2×4 DataFrame
Row sex outcome lower upper
Cat… Float64 Float64 Float64
1 Boy 7.9524 7.36768 8.53712
2 Girl 7.0564 6.49906 7.61374
plot(
    combine(groupby(kfm, :sex), :dl_milk => cis => AsTable),
    x = :sex, y = :outcome, ymin = :lower, ymax = :upper,
    Scale.x_discrete(levels=["Boy", "Girl"]),
    Geom.errorbar, Stat.dodge, Geom.bar(position = :dodge),
    Guide.xlabel(""),
    Guide.ylabel("Breast-milk intake (dl/day)")
)
Boy Girl h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? 0 2 4 6 8 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00 6.05 6.10 6.15 6.20 6.25 6.30 6.35 6.40 6.45 6.50 6.55 6.60 6.65 6.70 6.75 6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 7.30 7.35 7.40 7.45 7.50 7.55 7.60 7.65 7.70 7.75 7.80 7.85 7.90 7.95 8.00 8.05 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 9.05 9.10 9.15 9.20 9.25 9.30 9.35 9.40 9.45 9.50 9.55 9.60 9.65 9.70 9.75 9.80 9.85 9.90 9.95 10.00 0 10 Breast-milk intake (dl/day)
Figure 23: Comparison of daily breast-milk intake by sex.
combine(groupby(birth, [:smoke, :Race]), :bwt => cis => AsTable)
4×5 DataFrame
Row smoke Race outcome lower upper
Cat… Cat… Float64 Float64 Float64
1 Non-smoker White 3428.75 3218.93 3638.57
2 Non-smoker Non-white 2824.51 2664.85 2984.17
3 Smoker White 2826.85 2656.57 2997.12
4 Smoker Non-white 2642.09 2336.65 2947.54
plot(
    combine(groupby(birth, [:smoke, :Race]), :bwt => cis => AsTable),
    x = :Race, y = :outcome, color = :smoke, 
    ymin = :lower, ymax = :upper,
    Scale.x_discrete(levels=["White", "Non-white"]),
    Geom.errorbar, Stat.dodge, 
    Geom.bar(position = :dodge),
    Guide.xlabel(""),
    Guide.ylabel("Birth weight (g)"),
    Guide.colorkey(title="", pos=[0.8w, -0.4h])
  )
White Non-white h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? Non-smoker Smoker 0 1000 2000 3000 4000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800 820 840 860 880 900 920 940 960 980 1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200 1220 1240 1260 1280 1300 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 2120 2140 2160 2180 2200 2220 2240 2260 2280 2300 2320 2340 2360 2380 2400 2420 2440 2460 2480 2500 2520 2540 2560 2580 2600 2620 2640 2660 2680 2700 2720 2740 2760 2780 2800 2820 2840 2860 2880 2900 2920 2940 2960 2980 3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200 3220 3240 3260 3280 3300 3320 3340 3360 3380 3400 3420 3440 3460 3480 3500 3520 3540 3560 3580 3600 3620 3640 3660 3680 3700 3720 3740 3760 3780 3800 3820 3840 3860 3880 3900 3920 3940 3960 3980 4000 0 5000 Birth weight (g)
Figure 24: Comparison of birth weight by ethnicity and smoking status.